EASYTUTORGUIDE

Practical tutorials, tools, courses, digital skills, and business promotion.

Free Learning
Google Translate — English / فارسی / العربية
EasyTutorGuide LogoLearn, Build, & Grow

Chapter 45: Probability, Predictions, and Comparing Events

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
Advertisement area — AdSense / Auto Ads

Chapter Overview

This chapter teaches Probability, Predictions, and Comparing Events in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Probability meaning (The mean is found by adding all values and dividing by the number of values.)
  • Outcome (Outcome is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Event (Event is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Sample space (A sample is a smaller group selected from a population.)
  • Certain and impossible events (Certain and impossible events is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Likely and unlikely events (Likely and unlikely events is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

45.1 Probability meaning

The mean is found by adding all values and dividing by the number of values. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the mean of [4, 6, 8, 10].

  1. Add the values to get 28.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 2

Problem: Find the mean of [5, 7, 7, 9, 12].

  1. Add the values to get 40.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 8

Worked Example 3

Problem: Find the mean of [3, 5, 8, 8, 11].

  1. Add the values to get 35.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 4

Problem: Find the mean of [10, 12, 14, 16].

  1. Add the values to get 52.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 13

Worked Example 5

Problem: Find the mean of [2, 4, 6, 8, 10].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 6

Problem: Find the mean of [1, 5, 5, 6, 13].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 7

Problem: Find the mean of [20, 25, 25, 30].

  1. Add the values to get 100.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 25

Worked Example 8

Problem: Find the mean of [7, 8, 9, 10, 11].

  1. Add the values to get 45.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 9

Worked Example 9

Problem: Find the mean of [3, 3, 4, 5, 9].

  1. Add the values to get 24.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 4.8

Worked Example 10

Problem: Find the mean of [12, 15, 18, 21].

  1. Add the values to get 66.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 16.5

Practice Exercise

Create one new Grade 6 problem about Probability meaning. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is counting favourable outcomes but forgetting to count all possible outcomes.

45.2 Outcome

Outcome is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Outcome. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

45.3 Event

Event is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Event. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

45.4 Sample space

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Sample space. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

45.5 Certain and impossible events

Certain and impossible events is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Certain and impossible events. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

45.6 Likely and unlikely events

Likely and unlikely events is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Likely and unlikely events. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

45.7 Probability as a fraction

A fraction represents equal parts of a whole, set, or quantity. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide 1 by 2.

Very beginner explanation: The fraction bar means division.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide 2 by 3.

Very beginner explanation: The fraction bar means division.

Answer: 0.667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide 3 by 5.

Very beginner explanation: The fraction bar means division.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide 5 by 8.

Very beginner explanation: The fraction bar means division.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide 7 by 10.

Very beginner explanation: The fraction bar means division.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide 4 by 9.

Very beginner explanation: The fraction bar means division.

Answer: 0.444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide 5 by 6.

Very beginner explanation: The fraction bar means division.

Answer: 0.833

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide 3 by 4.

Very beginner explanation: The fraction bar means division.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide 2 by 5.

Very beginner explanation: The fraction bar means division.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide 7 by 12.

Very beginner explanation: The fraction bar means division.

Answer: 0.583

Practice Exercise

Create one new Grade 6 problem about Probability as a fraction. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is combining numerators and denominators without first applying the correct fraction rule.

45.8 Probability as a percent

Percent means 'per hundred' and compares a quantity with 100 equal parts. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find 1% of 80.

  1. Think of 1% as 1/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 0.8

Worked Example 2

Problem: Find 5% of 120.

  1. Think of 5% as 5/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6

Worked Example 3

Problem: Find 10% of 64.

  1. Think of 10% as 10/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6.4

Worked Example 4

Problem: Find 20% of 250.

  1. Think of 20% as 20/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 50

Worked Example 5

Problem: Find 25% of 96.

  1. Think of 25% as 25/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 24

Worked Example 6

Problem: Find 50% of 40.

  1. Think of 50% as 50/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 20

Worked Example 7

Problem: Find 75% of 200.

  1. Think of 75% as 75/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 150

Worked Example 8

Problem: Find 15% of 60.

  1. Think of 15% as 15/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 9

Worked Example 9

Problem: Find 30% of 150.

  1. Think of 30% as 30/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 45

Worked Example 10

Problem: Find 40% of 90.

  1. Think of 40% as 40/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 36

Practice Exercise

Create one new Grade 6 problem about Probability as a percent. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.

45.9 One-in-n language

One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use One-in-n language to analyze the values 28 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use One-in-n language to analyze the values 4 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use One-in-n language to analyze the values 26 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use One-in-n language to analyze the values 29 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use One-in-n language to analyze the values 9 and 3. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use One-in-n language to analyze the values 4 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use One-in-n language to analyze the values 4 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use One-in-n language to analyze the values 14 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use One-in-n language to analyze the values 21 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use One-in-n language to analyze the values 11 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about One-in-n language. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

45.10 Experimental probability

Probability describes how likely an event is to happen. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Experimental probability. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is counting favourable outcomes but forgetting to count all possible outcomes.

45.11 Theoretical probability introduction

Probability describes how likely an event is to happen. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Theoretical probability introduction. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is counting favourable outcomes but forgetting to count all possible outcomes.

45.12 Comparing event probabilities

Comparing event probabilities is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Comparing event probabilities. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

45.13 Making predictions

Making predictions is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Making predictions. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

45.14 Informed decisions using probability

Probability describes how likely an event is to happen. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Informed decisions using probability. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is counting favourable outcomes but forgetting to count all possible outcomes.

Advertisement area — AdSense / Auto Ads

30 Review Questions and Answers

Q1. What is important to understand about Probability meaning?

Answer: The mean is found by adding all values and dividing by the number of values.

Q2. What is important to understand about Outcome?

Answer: Outcome is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q3. What is important to understand about Event?

Answer: Event is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q4. What is important to understand about Sample space?

Answer: A sample is a smaller group selected from a population.

Q5. What is important to understand about Certain and impossible events?

Answer: Certain and impossible events is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q6. What is important to understand about Likely and unlikely events?

Answer: Likely and unlikely events is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q7. What is important to understand about Probability as a fraction?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q8. What is important to understand about Probability as a percent?

Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.

Q9. What is important to understand about One-in-n language?

Answer: One-in-n language is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q10. What is important to understand about Experimental probability?

Answer: Probability describes how likely an event is to happen.

Q11. What is important to understand about Theoretical probability introduction?

Answer: Probability describes how likely an event is to happen.

Q12. What is important to understand about Comparing event probabilities?

Answer: Comparing event probabilities is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. What is important to understand about Making predictions?

Answer: Making predictions is a Grade 6 mathematics idea in Probability, Predictions, and Comparing Events. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q14. What is important to understand about Informed decisions using probability?

Answer: Probability describes how likely an event is to happen.

Q15. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q16. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q17. Why do units matter?

Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.

Q18. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q19. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.

Q20. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the relationship connecting them.

Q21. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q22. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.

Q23. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q24. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q25. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q26. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q27. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q28. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q29. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.

Q30. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.