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Chapter 47: Probability as Fractions and on a Probability Line

Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.

Grade 5Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
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Chapter Overview

This chapter teaches Probability as Fractions and on a Probability Line with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

  • Outcomes and events (a Grade 5 idea used in this chapter)
  • Impossible and certain events (a Grade 5 idea used in this chapter)
  • Probability from 0 to 1 (a Grade 5 idea used in this chapter)
  • Writing probability as a fraction (a Grade 5 idea used in this chapter)
  • Equally likely outcomes (a Grade 5 idea used in this chapter)
  • Probability of a fair coin event (a Grade 5 idea used in this chapter)
  • Probability of a fair number cube event (a Grade 5 idea used in this chapter)
  • Plotting probability on a line (a Grade 5 idea used in this chapter)
  • Using probability to make predictions (a Grade 5 idea used in this chapter)
  • Using probability for decisions (a Grade 5 idea used in this chapter)

How to Learn This Chapter

Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

47.1 Outcomes and events

Outcomes and events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Outcomes and events?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Outcomes and events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Outcomes and events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Worked Example 2

Problem: What should you identify first before solving a problem about Outcomes and events?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Outcomes and events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Outcomes and events.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Outcomes and events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Outcomes and events problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Outcomes and events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Outcomes and events.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Outcomes and events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Outcomes and events can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. Favourable outcomes = 3.
  2. Total equally likely outcomes = 6.
  3. Probability = 3/6.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 7

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

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 2.
  3. Probability = 1/2.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw red from 5 red and 3 blue counters.

  1. Favourable outcomes = 5.
  2. Total equally likely outcomes = 8.
  3. Probability = 5/8.
  4. Simplify if possible.

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

Answer: 5/8

Worked Example 9

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

  1. Favourable outcomes = 2.
  2. Total equally likely outcomes = 4.
  3. Probability = 2/4.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 10

Problem: Find the probability to spin section 1 on four equal sections.

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 4.
  3. Probability = 1/4.
  4. Simplify if possible.

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

Answer: 1/4

Practice Exercise

Create one new question about Outcomes and events. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

47.2 Impossible and certain events

Impossible and certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Impossible and certain events?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Impossible and certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Impossible and certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Worked Example 2

Problem: What should you identify first before solving a problem about Impossible and certain events?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Impossible and certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Impossible and certain events.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Impossible and certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Impossible and certain events problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Impossible and certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Impossible and certain events.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Impossible and certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Impossible and certain events can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. Favourable outcomes = 3.
  2. Total equally likely outcomes = 6.
  3. Probability = 3/6.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 7

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

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 2.
  3. Probability = 1/2.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw red from 5 red and 3 blue counters.

  1. Favourable outcomes = 5.
  2. Total equally likely outcomes = 8.
  3. Probability = 5/8.
  4. Simplify if possible.

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

Answer: 5/8

Worked Example 9

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

  1. Favourable outcomes = 2.
  2. Total equally likely outcomes = 4.
  3. Probability = 2/4.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 10

Problem: Find the probability to spin section 1 on four equal sections.

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 4.
  3. Probability = 1/4.
  4. Simplify if possible.

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

Answer: 1/4

Practice Exercise

Create one new question about Impossible and certain events. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

47.3 Probability from 0 to 1

Probability from 0 to 1 describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Probability from 0 to 1?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Probability from 0 to 1 describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Probability from 0 to 1 describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Worked Example 2

Problem: What should you identify first before solving a problem about Probability from 0 to 1?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Probability from 0 to 1 describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Probability from 0 to 1.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Probability from 0 to 1 describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Probability from 0 to 1 problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Probability from 0 to 1 describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Probability from 0 to 1.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Probability from 0 to 1 describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Probability from 0 to 1 can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. Favourable outcomes = 3.
  2. Total equally likely outcomes = 6.
  3. Probability = 3/6.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 7

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

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 2.
  3. Probability = 1/2.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw red from 5 red and 3 blue counters.

  1. Favourable outcomes = 5.
  2. Total equally likely outcomes = 8.
  3. Probability = 5/8.
  4. Simplify if possible.

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

Answer: 5/8

Worked Example 9

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

  1. Favourable outcomes = 2.
  2. Total equally likely outcomes = 4.
  3. Probability = 2/4.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 10

Problem: Find the probability to spin section 1 on four equal sections.

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 4.
  3. Probability = 1/4.
  4. Simplify if possible.

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

Answer: 1/4

Practice Exercise

Create one new question about Probability from 0 to 1. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

47.4 Writing probability as a fraction

Writing probability as a fraction focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Writing probability as a fraction?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Writing probability as a fraction focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Answer: Writing probability as a fraction focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Worked Example 2

Problem: What should you identify first before solving a problem about Writing probability as a fraction?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Writing probability as a fraction focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Writing probability as a fraction.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Writing probability as a fraction focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Writing probability as a fraction problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Writing probability as a fraction focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Writing probability as a fraction.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Writing probability as a fraction focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Answer: Writing probability as a fraction can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Write 1/3 as a decimal.

  1. A fraction bar means division.
  2. Divide 1 by 3.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.3333

Worked Example 7

Problem: Write 2/5 as a decimal.

  1. A fraction bar means division.
  2. Divide 2 by 5.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.4

Worked Example 8

Problem: Write 3/8 as a decimal.

  1. A fraction bar means division.
  2. Divide 3 by 8.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.375

Worked Example 9

Problem: Write 5/12 as a decimal.

  1. A fraction bar means division.
  2. Divide 5 by 12.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.4167

Worked Example 10

Problem: Write 7/9 as a decimal.

  1. A fraction bar means division.
  2. Divide 7 by 9.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.7778

Practice Exercise

Create one new question about Writing probability as a fraction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

47.5 Equally likely outcomes

Equally likely outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Equally likely outcomes?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Equally likely outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Equally likely outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Worked Example 2

Problem: What should you identify first before solving a problem about Equally likely outcomes?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Equally likely outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Equally likely outcomes.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Equally likely outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Equally likely outcomes problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Equally likely outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Equally likely outcomes.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Equally likely outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Equally likely outcomes can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. Favourable outcomes = 3.
  2. Total equally likely outcomes = 6.
  3. Probability = 3/6.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 7

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

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 2.
  3. Probability = 1/2.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw red from 5 red and 3 blue counters.

  1. Favourable outcomes = 5.
  2. Total equally likely outcomes = 8.
  3. Probability = 5/8.
  4. Simplify if possible.

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

Answer: 5/8

Worked Example 9

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

  1. Favourable outcomes = 2.
  2. Total equally likely outcomes = 4.
  3. Probability = 2/4.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 10

Problem: Find the probability to spin section 1 on four equal sections.

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 4.
  3. Probability = 1/4.
  4. Simplify if possible.

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

Answer: 1/4

Practice Exercise

Create one new question about Equally likely outcomes. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

47.6 Probability of a fair coin event

Probability of a fair coin event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Probability of a fair coin event?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Probability of a fair coin event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Probability of a fair coin event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Worked Example 2

Problem: What should you identify first before solving a problem about Probability of a fair coin event?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Probability of a fair coin event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Probability of a fair coin event.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Probability of a fair coin event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Probability of a fair coin event problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Probability of a fair coin event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Probability of a fair coin event.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Probability of a fair coin event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Probability of a fair coin event can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. Favourable outcomes = 3.
  2. Total equally likely outcomes = 6.
  3. Probability = 3/6.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 7

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

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 2.
  3. Probability = 1/2.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw red from 5 red and 3 blue counters.

  1. Favourable outcomes = 5.
  2. Total equally likely outcomes = 8.
  3. Probability = 5/8.
  4. Simplify if possible.

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

Answer: 5/8

Worked Example 9

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

  1. Favourable outcomes = 2.
  2. Total equally likely outcomes = 4.
  3. Probability = 2/4.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 10

Problem: Find the probability to spin section 1 on four equal sections.

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 4.
  3. Probability = 1/4.
  4. Simplify if possible.

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

Answer: 1/4

Practice Exercise

Create one new question about Probability of a fair coin event. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

47.7 Probability of a fair number cube event

Probability of a fair number cube event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Probability of a fair number cube event?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Probability of a fair number cube event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Probability of a fair number cube event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Worked Example 2

Problem: What should you identify first before solving a problem about Probability of a fair number cube event?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Probability of a fair number cube event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Probability of a fair number cube event.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Probability of a fair number cube event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Probability of a fair number cube event problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Probability of a fair number cube event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Probability of a fair number cube event.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Probability of a fair number cube event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Probability of a fair number cube event can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. Favourable outcomes = 3.
  2. Total equally likely outcomes = 6.
  3. Probability = 3/6.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 7

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

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 2.
  3. Probability = 1/2.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw red from 5 red and 3 blue counters.

  1. Favourable outcomes = 5.
  2. Total equally likely outcomes = 8.
  3. Probability = 5/8.
  4. Simplify if possible.

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

Answer: 5/8

Worked Example 9

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

  1. Favourable outcomes = 2.
  2. Total equally likely outcomes = 4.
  3. Probability = 2/4.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 10

Problem: Find the probability to spin section 1 on four equal sections.

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 4.
  3. Probability = 1/4.
  4. Simplify if possible.

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

Answer: 1/4

Practice Exercise

Create one new question about Probability of a fair number cube event. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

47.8 Plotting probability on a line

Plotting probability on a line describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Plotting probability on a line?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Plotting probability on a line describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Plotting probability on a line describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Worked Example 2

Problem: What should you identify first before solving a problem about Plotting probability on a line?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Plotting probability on a line describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Plotting probability on a line.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Plotting probability on a line describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Plotting probability on a line problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Plotting probability on a line describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Plotting probability on a line.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Plotting probability on a line describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Plotting probability on a line can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. Favourable outcomes = 3.
  2. Total equally likely outcomes = 6.
  3. Probability = 3/6.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 7

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

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 2.
  3. Probability = 1/2.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw red from 5 red and 3 blue counters.

  1. Favourable outcomes = 5.
  2. Total equally likely outcomes = 8.
  3. Probability = 5/8.
  4. Simplify if possible.

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

Answer: 5/8

Worked Example 9

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

  1. Favourable outcomes = 2.
  2. Total equally likely outcomes = 4.
  3. Probability = 2/4.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 10

Problem: Find the probability to spin section 1 on four equal sections.

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 4.
  3. Probability = 1/4.
  4. Simplify if possible.

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

Answer: 1/4

Practice Exercise

Create one new question about Plotting probability on a line. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

47.9 Using probability to make predictions

Using probability to make predictions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Using probability to make predictions?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Using probability to make predictions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Using probability to make predictions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Worked Example 2

Problem: What should you identify first before solving a problem about Using probability to make predictions?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Using probability to make predictions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Using probability to make predictions.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Using probability to make predictions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Using probability to make predictions problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Using probability to make predictions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Using probability to make predictions.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Using probability to make predictions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Using probability to make predictions can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. Favourable outcomes = 3.
  2. Total equally likely outcomes = 6.
  3. Probability = 3/6.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 7

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

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 2.
  3. Probability = 1/2.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw red from 5 red and 3 blue counters.

  1. Favourable outcomes = 5.
  2. Total equally likely outcomes = 8.
  3. Probability = 5/8.
  4. Simplify if possible.

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

Answer: 5/8

Worked Example 9

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

  1. Favourable outcomes = 2.
  2. Total equally likely outcomes = 4.
  3. Probability = 2/4.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 10

Problem: Find the probability to spin section 1 on four equal sections.

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 4.
  3. Probability = 1/4.
  4. Simplify if possible.

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

Answer: 1/4

Practice Exercise

Create one new question about Using probability to make predictions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

47.10 Using probability for decisions

Using probability for decisions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Using probability for decisions?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Using probability for decisions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Using probability for decisions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Worked Example 2

Problem: What should you identify first before solving a problem about Using probability for decisions?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Using probability for decisions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Using probability for decisions.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Using probability for decisions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Using probability for decisions problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Using probability for decisions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Using probability for decisions.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Using probability for decisions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Answer: Using probability for decisions can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. Favourable outcomes = 3.
  2. Total equally likely outcomes = 6.
  3. Probability = 3/6.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 7

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

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 2.
  3. Probability = 1/2.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw red from 5 red and 3 blue counters.

  1. Favourable outcomes = 5.
  2. Total equally likely outcomes = 8.
  3. Probability = 5/8.
  4. Simplify if possible.

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

Answer: 5/8

Worked Example 9

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

  1. Favourable outcomes = 2.
  2. Total equally likely outcomes = 4.
  3. Probability = 2/4.
  4. Simplify if possible.

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

Answer: 1/2

Worked Example 10

Problem: Find the probability to spin section 1 on four equal sections.

  1. Favourable outcomes = 1.
  2. Total equally likely outcomes = 4.
  3. Probability = 1/4.
  4. Simplify if possible.

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

Answer: 1/4

Practice Exercise

Create one new question about Using probability for decisions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

Chapter Notes, Practice, and Common Mistakes

Chapter Notes

  • Read the question before calculating.
  • Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
  • Show the reasoning and check the final answer with a second method when possible.

Extra Practice

  1. Create and solve one original problem about Outcomes and events.
  2. Create and solve one original problem about Impossible and certain events.
  3. Create and solve one original problem about Probability from 0 to 1.
  4. Create and solve one original problem about Writing probability as a fraction.
  5. Create and solve one original problem about Equally likely outcomes.
  6. Create and solve one original problem about Probability of a fair coin event.

Common Mistakes

  • Skipping the meaning and trying to memorize a rule only.
  • Using the wrong operation because the question was not read completely.
  • Ignoring units, labels, place values, or the context of the problem.
  • Not estimating or checking whether the final answer is reasonable.
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30 Review Questions and Answers

Q1. What is the key idea in Outcomes and events?

Answer: Outcomes and events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Q2. What is the key idea in Impossible and certain events?

Answer: Impossible and certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Q3. What is the key idea in Probability from 0 to 1?

Answer: Probability from 0 to 1 describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Q4. What is the key idea in Writing probability as a fraction?

Answer: Writing probability as a fraction focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Q5. What is the key idea in Equally likely outcomes?

Answer: Equally likely outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Q6. What is the key idea in Probability of a fair coin event?

Answer: Probability of a fair coin event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Q7. What is the key idea in Probability of a fair number cube event?

Answer: Probability of a fair number cube event describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Q8. What is the key idea in Plotting probability on a line?

Answer: Plotting probability on a line describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Q9. What is the key idea in Using probability to make predictions?

Answer: Using probability to make predictions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Q10. What is the key idea in Using probability for decisions?

Answer: Using probability for decisions describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.

Q11. Why should you estimate before or after a calculation?

Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.

Q12. Why are labels and units important?

Answer: They show what a number represents and help prevent mixing unlike quantities.

Q13. How can a diagram help solve a problem?

Answer: A diagram makes quantities and relationships visible before calculation.

Q14. How can inverse operations check an answer?

Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.

Q15. Why should you show steps?

Answer: Showing steps makes reasoning clear and helps find where an error happened.

Q16. What should you do after making a mistake?

Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.

Q17. How can a number line support reasoning?

Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.

Q18. When is a table useful?

Answer: A table organizes related values so patterns and comparisons are easier to see.

Q19. When is a graph useful?

Answer: A graph makes trends, comparisons, locations, or data patterns visible.

Q20. How do you decide which operation to use?

Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.

Q21. Why should you check place value?

Answer: A digit or decimal has a different value depending on its position.

Q22. What makes an answer reasonable?

Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.

Q23. How can you explain mathematical reasoning clearly?

Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.

Q24. Why can more than one strategy be correct?

Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.

Q25. How should you approach a difficult Grade 5 problem?

Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.

Q26. How can you practise Probability as Fractions and on a Probability Line effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q27. How can you practise Probability as Fractions and on a Probability Line effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q28. How can you practise Probability as Fractions and on a Probability Line effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q29. How can you practise Probability as Fractions and on a Probability Line effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q30. How can you practise Probability as Fractions and on a Probability Line effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.