Chapter 48: Chance and Likelihood Review
Learn Grade 3 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Chance and Likelihood Review with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Impossible events (a Grade 3 idea used in this chapter)
- Unlikely events (a Grade 3 idea used in this chapter)
- Equally likely outcomes (a Grade 3 idea used in this chapter)
- Likely events (a Grade 3 idea used in this chapter)
- Certain events (a Grade 3 idea used in this chapter)
- Ordering events by likelihood (a Grade 3 idea used in this chapter)
- Simple coin outcomes (a Grade 3 idea used in this chapter)
- Simple spinner outcomes (a Grade 3 idea used in this chapter)
- Using likelihood words in decisions (a Grade 3 idea used in this chapter)
- Explaining a chance prediction (a Grade 3 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.
48.1 Impossible events
Impossible 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 events?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Impossible events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Impossible 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 events?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Impossible 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 events.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Impossible 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 events problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Impossible 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 events.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Impossible events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Impossible 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.
- 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 events. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
48.2 Unlikely events
Unlikely 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 Unlikely events?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Unlikely events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Unlikely 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 Unlikely events?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Unlikely 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 Unlikely events.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Unlikely 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 Unlikely events problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Unlikely 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 Unlikely events.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Unlikely events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Unlikely 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.
- 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 events. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
48.3 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?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- 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?
- Read the complete problem.
- Mark the information that is given.
- 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.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- 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?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- 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.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- 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.
- 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 Equally likely outcomes. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
48.4 Likely events
Likely 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 Likely events?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Likely events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Likely 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 Likely events?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Likely 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 Likely events.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Likely 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 Likely events problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Likely 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 Likely events.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Likely events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Likely 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.
- 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 events. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
48.5 Certain events
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 Certain events?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: 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 Certain events?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: 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 Certain events.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: 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 Certain events problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: 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 Certain events.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Certain events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: 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.
- 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 events. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
48.6 Ordering events by likelihood
Ordering events by likelihood 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 Ordering events by likelihood?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Ordering events by likelihood describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Ordering events by likelihood 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 Ordering events by likelihood?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Ordering events by likelihood 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 Ordering events by likelihood.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Ordering events by likelihood 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 Ordering events by likelihood problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Ordering events by likelihood 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 Ordering events by likelihood.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Ordering events by likelihood describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Ordering events by likelihood 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.
- 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 Ordering events by likelihood. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
48.7 Simple coin outcomes
Simple coin 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 Simple coin outcomes?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Simple coin outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Simple coin 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 Simple coin outcomes?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Simple coin 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 Simple coin outcomes.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Simple coin 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 Simple coin outcomes problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Simple coin 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 Simple coin outcomes.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Simple coin outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Simple coin 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.
- 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 Simple coin outcomes. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
48.8 Simple spinner outcomes
Simple spinner 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 Simple spinner outcomes?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Simple spinner outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Simple spinner 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 Simple spinner outcomes?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Simple spinner 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 Simple spinner outcomes.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Simple spinner 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 Simple spinner outcomes problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Simple spinner 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 Simple spinner outcomes.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Simple spinner outcomes describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Answer: Simple spinner 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.
- 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 Simple spinner outcomes. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
48.9 Using likelihood words in decisions
Using likelihood words in decisions is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
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 likelihood words in decisions?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Using likelihood words in decisions is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Using likelihood words in decisions is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Using likelihood words in decisions?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Using likelihood words in decisions is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Using likelihood words in decisions.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Using likelihood words in decisions is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
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 likelihood words in decisions problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Using likelihood words in decisions is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
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 likelihood words in decisions.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Using likelihood words in decisions is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Using likelihood words in decisions can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Using likelihood words in decisions in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Using likelihood words in decisions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Using likelihood words in decisions and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Using likelihood words in decisions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Using likelihood words in decisions using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Using likelihood words in decisions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Using likelihood words in decisions problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Using likelihood words in decisions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Using likelihood words in decisions could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Using likelihood words in decisions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Using likelihood words in decisions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
48.10 Explaining a chance prediction
Explaining a chance prediction is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
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 Explaining a chance prediction?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Explaining a chance prediction is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Explaining a chance prediction is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Explaining a chance prediction?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Explaining a chance prediction is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Explaining a chance prediction.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Explaining a chance prediction is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
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 Explaining a chance prediction problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Explaining a chance prediction is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
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 Explaining a chance prediction.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Explaining a chance prediction is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Explaining a chance prediction can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Explaining a chance prediction in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Explaining a chance prediction becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Explaining a chance prediction and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Explaining a chance prediction becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Explaining a chance prediction using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Explaining a chance prediction becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Explaining a chance prediction problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Explaining a chance prediction becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Explaining a chance prediction could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Explaining a chance prediction becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Explaining a chance prediction. 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
- Create and solve one original problem about Impossible events.
- Create and solve one original problem about Unlikely events.
- Create and solve one original problem about Equally likely outcomes.
- Create and solve one original problem about Likely events.
- Create and solve one original problem about Certain events.
- Create and solve one original problem about Ordering events by likelihood.
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.
30 Review Questions and Answers
Q1. What is the key idea in Impossible events?
Answer: Impossible 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 Unlikely events?
Answer: Unlikely 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 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.
Q4. What is the key idea in Likely events?
Answer: Likely events describes chance using fractions and experiments. Learners compare what mathematics predicts with what actually happens in repeated trials.
Q5. What is the key idea in Certain events?
Answer: Certain events 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 Ordering events by likelihood?
Answer: Ordering events by likelihood 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 Simple coin outcomes?
Answer: Simple coin outcomes 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 Simple spinner outcomes?
Answer: Simple spinner outcomes 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 likelihood words in decisions?
Answer: Using likelihood words in decisions is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q10. What is the key idea in Explaining a chance prediction?
Answer: Explaining a chance prediction is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
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 3 problem?
Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.
Q26. How can you practise Chance and Likelihood Review 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 Chance and Likelihood Review 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 Chance and Likelihood Review 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 Chance and Likelihood Review 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 Chance and Likelihood Review effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.