Chapter 42: Probability Foundations
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Probability Foundations with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Percent (a ratio out of 100)
- Sample (a smaller group selected from a population)
- Independent Events (events whose probabilities do not affect each other)
- Dependent Events (events where one outcome changes the probability of another)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
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.
42.1 Probability
Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Roll an even number on a fair die
- Favourable outcomes=3.
- Total equally likely outcomes=6.
- P=3/6.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability .
Answer: 3/6
Worked Example 2
Problem: Flip heads on a fair coin
- Favourable outcomes=1.
- Total equally likely outcomes=2.
- P=1/2.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability .
Answer: 1/2
Worked Example 3
Problem: Draw red from 5 red and 3 blue marbles
- Favourable outcomes=5.
- Total equally likely outcomes=8.
- P=5/8.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability .
Answer: 5/8
Worked Example 4
Problem: Choose a vowel from A,B,C,E
- Favourable outcomes=2.
- Total equally likely outcomes=4.
- P=2/4.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability .
Answer: 2/4
Worked Example 5
Problem: Spin 1 on a 4-equal-section spinner
- Favourable outcomes=1.
- Total equally likely outcomes=4.
- P=1/4.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability .
Answer: 1/4
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.2 Outcome
Outcome is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Roll an even number on a fair die
- Favourable outcomes=3.
- Total equally likely outcomes=6.
- P=3/6.
Very beginner explanation: Outcome is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3/6
Worked Example 2
Problem: Flip heads on a fair coin
- Favourable outcomes=1.
- Total equally likely outcomes=2.
- P=1/2.
Very beginner explanation: Outcome is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/2
Worked Example 3
Problem: Draw red from 5 red and 3 blue marbles
- Favourable outcomes=5.
- Total equally likely outcomes=8.
- P=5/8.
Very beginner explanation: Outcome is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5/8
Worked Example 4
Problem: Choose a vowel from A,B,C,E
- Favourable outcomes=2.
- Total equally likely outcomes=4.
- P=2/4.
Very beginner explanation: Outcome is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2/4
Worked Example 5
Problem: Spin 1 on a 4-equal-section spinner
- Favourable outcomes=1.
- Total equally likely outcomes=4.
- P=1/4.
Very beginner explanation: Outcome is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/4
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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 Outcome. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.3 Event
Event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Roll an even number on a fair die
- Favourable outcomes=3.
- Total equally likely outcomes=6.
- P=3/6.
Very beginner explanation: Event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3/6
Worked Example 2
Problem: Flip heads on a fair coin
- Favourable outcomes=1.
- Total equally likely outcomes=2.
- P=1/2.
Very beginner explanation: Event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/2
Worked Example 3
Problem: Draw red from 5 red and 3 blue marbles
- Favourable outcomes=5.
- Total equally likely outcomes=8.
- P=5/8.
Very beginner explanation: Event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5/8
Worked Example 4
Problem: Choose a vowel from A,B,C,E
- Favourable outcomes=2.
- Total equally likely outcomes=4.
- P=2/4.
Very beginner explanation: Event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2/4
Worked Example 5
Problem: Spin 1 on a 4-equal-section spinner
- Favourable outcomes=1.
- Total equally likely outcomes=4.
- P=1/4.
Very beginner explanation: Event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/4
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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 Event. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.4 Sample space
A sample is a smaller group selected from a population. This topic focuses on Sample space .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample space .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample space .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample space .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample space .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Sample space .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Sample space. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.5 Certain event
Certain event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Roll an even number on a fair die
- Favourable outcomes=3.
- Total equally likely outcomes=6.
- P=3/6.
Very beginner explanation: Certain event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3/6
Worked Example 2
Problem: Flip heads on a fair coin
- Favourable outcomes=1.
- Total equally likely outcomes=2.
- P=1/2.
Very beginner explanation: Certain event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/2
Worked Example 3
Problem: Draw red from 5 red and 3 blue marbles
- Favourable outcomes=5.
- Total equally likely outcomes=8.
- P=5/8.
Very beginner explanation: Certain event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5/8
Worked Example 4
Problem: Choose a vowel from A,B,C,E
- Favourable outcomes=2.
- Total equally likely outcomes=4.
- P=2/4.
Very beginner explanation: Certain event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2/4
Worked Example 5
Problem: Spin 1 on a 4-equal-section spinner
- Favourable outcomes=1.
- Total equally likely outcomes=4.
- P=1/4.
Very beginner explanation: Certain event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/4
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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 Certain event. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.6 Impossible event
Impossible event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Roll an even number on a fair die
- Favourable outcomes=3.
- Total equally likely outcomes=6.
- P=3/6.
Very beginner explanation: Impossible event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3/6
Worked Example 2
Problem: Flip heads on a fair coin
- Favourable outcomes=1.
- Total equally likely outcomes=2.
- P=1/2.
Very beginner explanation: Impossible event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/2
Worked Example 3
Problem: Draw red from 5 red and 3 blue marbles
- Favourable outcomes=5.
- Total equally likely outcomes=8.
- P=5/8.
Very beginner explanation: Impossible event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5/8
Worked Example 4
Problem: Choose a vowel from A,B,C,E
- Favourable outcomes=2.
- Total equally likely outcomes=4.
- P=2/4.
Very beginner explanation: Impossible event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2/4
Worked Example 5
Problem: Spin 1 on a 4-equal-section spinner
- Favourable outcomes=1.
- Total equally likely outcomes=4.
- P=1/4.
Very beginner explanation: Impossible event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/4
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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 event. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.7 Likely event
Likely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Roll an even number on a fair die
- Favourable outcomes=3.
- Total equally likely outcomes=6.
- P=3/6.
Very beginner explanation: Likely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3/6
Worked Example 2
Problem: Flip heads on a fair coin
- Favourable outcomes=1.
- Total equally likely outcomes=2.
- P=1/2.
Very beginner explanation: Likely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/2
Worked Example 3
Problem: Draw red from 5 red and 3 blue marbles
- Favourable outcomes=5.
- Total equally likely outcomes=8.
- P=5/8.
Very beginner explanation: Likely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5/8
Worked Example 4
Problem: Choose a vowel from A,B,C,E
- Favourable outcomes=2.
- Total equally likely outcomes=4.
- P=2/4.
Very beginner explanation: Likely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2/4
Worked Example 5
Problem: Spin 1 on a 4-equal-section spinner
- Favourable outcomes=1.
- Total equally likely outcomes=4.
- P=1/4.
Very beginner explanation: Likely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/4
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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 Likely event. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.8 Unlikely event
Unlikely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Roll an even number on a fair die
- Favourable outcomes=3.
- Total equally likely outcomes=6.
- P=3/6.
Very beginner explanation: Unlikely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3/6
Worked Example 2
Problem: Flip heads on a fair coin
- Favourable outcomes=1.
- Total equally likely outcomes=2.
- P=1/2.
Very beginner explanation: Unlikely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/2
Worked Example 3
Problem: Draw red from 5 red and 3 blue marbles
- Favourable outcomes=5.
- Total equally likely outcomes=8.
- P=5/8.
Very beginner explanation: Unlikely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5/8
Worked Example 4
Problem: Choose a vowel from A,B,C,E
- Favourable outcomes=2.
- Total equally likely outcomes=4.
- P=2/4.
Very beginner explanation: Unlikely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2/4
Worked Example 5
Problem: Spin 1 on a 4-equal-section spinner
- Favourable outcomes=1.
- Total equally likely outcomes=4.
- P=1/4.
Very beginner explanation: Unlikely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/4
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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 Unlikely event. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.9 Probability as fraction
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Probability as fraction .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Probability as fraction .
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Probability as fraction .
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Probability as fraction .
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Probability as fraction .
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Probability as fraction .
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- 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.
- A fraction bar means division.
- 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.
- A fraction bar means division.
- 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.
- A fraction bar means division.
- 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.
- A fraction bar means division.
- 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 Probability as fraction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.10 Probability as decimal
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Probability as decimal .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Probability as decimal .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Probability as decimal .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Probability as decimal .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Probability as decimal .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Probability as decimal .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 3.8
Worked Example 7
Problem: Round 8.4 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 8.4
Worked Example 8
Problem: Round 12.05 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 12.1
Worked Example 9
Problem: Round 0.96 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 1
Worked Example 10
Problem: Round 5.125 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 5.1
Practice Exercise
Create one new question about Probability as decimal. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.11 Probability as percent
Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Probability as percent .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of 80.
- 10% = 0.1.
- 0.1×80=8.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Probability as percent .
Answer: 8
Worked Example 2
Problem: Find 25% of 60.
- 25% = 0.25.
- 0.25×60=15.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Probability as percent .
Answer: 15
Worked Example 3
Problem: Find 15% of 120.
- 15% = 0.15.
- 0.15×120=18.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Probability as percent .
Answer: 18
Worked Example 4
Problem: Find 5% of 250.
- 5% = 0.05.
- 0.05×250=12.5.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Probability as percent .
Answer: 12.5
Worked Example 5
Problem: Find 13% of 75.
- 13% = 0.13.
- 0.13×75=9.75.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Probability as percent .
Answer: 9.75
Worked Example 6
Problem: Find 10% of 90.
- 10% = 0.1.
- 0.1 × 90 = 9.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 9
Worked Example 7
Problem: Find 25% of 64.
- 25% = 0.25.
- 0.25 × 64 = 16.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 16
Worked Example 8
Problem: Find 15% of 140.
- 15% = 0.15.
- 0.15 × 140 = 21.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 21
Worked Example 9
Problem: Find 5% of 260.
- 5% = 0.05.
- 0.05 × 260 = 13.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 13
Worked Example 10
Problem: Find 20% of 75.
- 20% = 0.2.
- 0.2 × 75 = 15.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 15
Practice Exercise
Create one new question about Probability as percent. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.12 Probability scale
Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability scale .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Scale factor 2; original side 6 cm. Find image side.
- Multiply 6 by 2.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability scale .
Answer: 12 cm
Worked Example 2
Problem: Scale factor 1.5; original side 8 cm. Find image side.
- Multiply 8 by 1.5.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability scale .
Answer: 12 cm
Worked Example 3
Problem: Scale factor 0.5; original side 14 cm. Find image side.
- Multiply 14 by 0.5.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability scale .
Answer: 7 cm
Worked Example 4
Problem: Scale factor 3; original side 5 cm. Find image side.
- Multiply 5 by 3.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability scale .
Answer: 15 cm
Worked Example 5
Problem: Scale factor 4; original side 2.5 cm. Find image side.
- Multiply 2.5 by 4.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability scale .
Answer: 10 cm
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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 scale. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.13 Complementary events introduction
Complementary events introduction is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Roll an even number on a fair die
- Favourable outcomes=3.
- Total equally likely outcomes=6.
- P=3/6.
Very beginner explanation: Complementary events introduction is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3/6
Worked Example 2
Problem: Flip heads on a fair coin
- Favourable outcomes=1.
- Total equally likely outcomes=2.
- P=1/2.
Very beginner explanation: Complementary events introduction is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/2
Worked Example 3
Problem: Draw red from 5 red and 3 blue marbles
- Favourable outcomes=5.
- Total equally likely outcomes=8.
- P=5/8.
Very beginner explanation: Complementary events introduction is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5/8
Worked Example 4
Problem: Choose a vowel from A,B,C,E
- Favourable outcomes=2.
- Total equally likely outcomes=4.
- P=2/4.
Very beginner explanation: Complementary events introduction is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2/4
Worked Example 5
Problem: Spin 1 on a 4-equal-section spinner
- Favourable outcomes=1.
- Total equally likely outcomes=4.
- P=1/4.
Very beginner explanation: Complementary events introduction is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/4
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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 Complementary events introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
42.14 Real-life probability
Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Real-life probability .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Roll an even number on a fair die
- Favourable outcomes=3.
- Total equally likely outcomes=6.
- P=3/6.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Real-life probability .
Answer: 3/6
Worked Example 2
Problem: Flip heads on a fair coin
- Favourable outcomes=1.
- Total equally likely outcomes=2.
- P=1/2.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Real-life probability .
Answer: 1/2
Worked Example 3
Problem: Draw red from 5 red and 3 blue marbles
- Favourable outcomes=5.
- Total equally likely outcomes=8.
- P=5/8.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Real-life probability .
Answer: 5/8
Worked Example 4
Problem: Choose a vowel from A,B,C,E
- Favourable outcomes=2.
- Total equally likely outcomes=4.
- P=2/4.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Real-life probability .
Answer: 2/4
Worked Example 5
Problem: Spin 1 on a 4-equal-section spinner
- Favourable outcomes=1.
- Total equally likely outcomes=4.
- P=1/4.
Very beginner explanation: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Real-life probability .
Answer: 1/4
Worked Example 6
Problem: Find the probability to roll an even number on a fair die.
- Favourable outcomes = 3.
- Total equally likely outcomes = 6.
- Probability = 3/6.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 2.
- Probability = 1/2.
- 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.
- Favourable outcomes = 5.
- Total equally likely outcomes = 8.
- Probability = 5/8.
- 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.
- Favourable outcomes = 2.
- Total equally likely outcomes = 4.
- Probability = 2/4.
- 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.
- Favourable outcomes = 1.
- Total equally likely outcomes = 4.
- Probability = 1/4.
- 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 Real-life probability. 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 complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Probability . Show your reasoning and check your answer.
- Create and solve a new question about Outcome . Show your reasoning and check your answer.
- Create and solve a new question about Event . Show your reasoning and check your answer.
- Create and solve a new question about Sample space . Show your reasoning and check your answer.
- Create and solve a new question about Certain event . Show your reasoning and check your answer.
- Create and solve a new question about Impossible event . Show your reasoning and check your answer.
- Create and solve a new question about Likely event . Show your reasoning and check your answer.
- Create and solve a new question about Unlikely event . Show your reasoning and check your answer.
- Create and solve a new question about Probability as fraction . Show your reasoning and check your answer.
- Create and solve a new question about Probability as decimal . Show your reasoning and check your answer.
- Create and solve a new question about Probability as percent . Show your reasoning and check your answer.
- Create and solve a new question about Probability scale . Show your reasoning and check your answer.
Common Mistakes
- Using a biased or unrepresentative sample.
- Reading graph scales incorrectly.
- Treating a misleading graph as trustworthy without checking the axes.
- Assuming dependent events are independent.
- Using percentages in a circle graph that do not total 100%.
30 Review Questions and Answers
Q1. What is important to remember about Probability?
Answer: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability.
Q2. What is important to remember about Outcome?
Answer: Outcome is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Event?
Answer: Event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q4. What is important to remember about Sample space?
Answer: A sample is a smaller group selected from a population. This topic focuses on Sample space.
Q5. What is important to remember about Certain event?
Answer: Certain event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Impossible event?
Answer: Impossible event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q7. What is important to remember about Likely event?
Answer: Likely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Unlikely event?
Answer: Unlikely event is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q9. What is important to remember about Probability as fraction?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Probability as fraction.
Q10. What is important to remember about Probability as decimal?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Probability as decimal.
Q11. What is important to remember about Probability as percent?
Answer: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Probability as percent.
Q12. What is important to remember about Probability scale?
Answer: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Probability scale.
Q13. What is important to remember about Complementary events introduction?
Answer: Complementary events introduction is an important Grade 7 idea in Probability Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q14. What is important to remember about Real-life probability?
Answer: Probability measures likelihood from 0 to 1, or from 0% to 100%. This topic focuses on Real-life probability.
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 prevent incompatible quantities from being mixed.
Q18. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q19. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, 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, check copied values, signs, units, formulas, and calculations.
Q23. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q24. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q25. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q26. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q27. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q28. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q29. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q30. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.