Free Grade 3 Introducing Relative Frequency Techniques Lessons
Free Grade 3 lessons for Introducing Relative Frequency Techniques: 12 real questions with a full answer key and worked solutions. Probability measures how likely something is, from 0 (impossible) to 1 (certain). P(event) = favourable outcomes ÷ total outcomes. For independent events, multiply.
Free
Foundation
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing relative frequency techniques
Identify introducing relative frequency techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing relative frequency techniques
Explain introducing relative frequency techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing relative frequency techniques
Calculate introducing relative frequency techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing relative frequency techniques
Compare introducing relative frequency techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Introducing Relative Frequency Techniques works
Probability measures how likely something is, from 0 (impossible) to 1 (certain). P(event) = favourable outcomes ÷ total outcomes. For independent events, multiply.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.A bag has 2 red, 2 blue and 3 green counters. One is picked at random. Find P(red).[1]
- 2.A bag has 1 red, 7 blue and 5 green counters. One is picked at random. Find P(red).[1]
- 3.A bag has 5 red, 5 blue and 5 green counters. One is picked at random. Find P(red).[1]
- 4.A bag has 4 red, 8 blue and 2 green counters. One is picked at random. Find P(red).[1]
- 5.A bag has 7 red, 6 blue and 1 green counters. One is picked at random. Find P(red) and P(not red).[2]
- 6.A bag has 7 red, 6 blue and 2 green counters. One is picked at random. Find P(red) and P(not red).[2]
- 7.A bag has 6 red, 2 blue and 5 green counters. One is picked at random. Find P(red) and P(not red).[2]
- 8.A bag has 8 red, 5 blue and 3 green counters. One is picked at random. Find P(red) and P(not red).[2]
- 9.A bag has 8 red and 5 blue counters. Two are picked with replacement. Find P(both red).[3]
- 10.A bag has 8 red and 4 blue counters. Two are picked with replacement. Find P(both red).[3]
- 11.A bag has 6 red and 8 blue counters. Two are picked with replacement. Find P(both red).[3]
- 12.A bag has 1 red and 4 blue counters. Two are picked with replacement. Find P(both red).[3]
Show answers and working
1. P(red) = 2/7
Total counters = 7. P(red) = 2/7 = 2/7.
2. P(red) = 1/13
Total counters = 13. P(red) = 1/13 = 1/13.
3. P(red) = 1/3
Total counters = 15. P(red) = 5/15 = 1/3.
4. P(red) = 2/7
Total counters = 14. P(red) = 4/14 = 2/7.
5. P(red) = 1/2, P(not red) = 1/2
Total counters = 14. P(red) = 7/14 = 1/2. P(not red) = 1 − 1/2 = 1/2.
6. P(red) = 7/15, P(not red) = 8/15
Total counters = 15. P(red) = 7/15 = 7/15. P(not red) = 1 − 7/15 = 8/15.
7. P(red) = 6/13, P(not red) = 7/13
Total counters = 13. P(red) = 6/13 = 6/13. P(not red) = 1 − 6/13 = 7/13.
8. P(red) = 1/2, P(not red) = 1/2
Total counters = 16. P(red) = 8/16 = 1/2. P(not red) = 1 − 1/2 = 1/2.
9. 64/169
P(red) = 8/13 each time. Independent, so multiply: 8/13 × 8/13 = 64/169.
10. 4/9
P(red) = 8/12 each time. Independent, so multiply: 8/12 × 8/12 = 4/9.
11. 9/49
P(red) = 6/14 each time. Independent, so multiply: 6/14 × 6/14 = 9/49.
12. 1/25
P(red) = 1/5 each time. Independent, so multiply: 1/5 × 1/5 = 1/25.
Worked examples
A bag has 4 red, 5 blue and 5 green counters. One is picked at random. Find P(red).
- Total counters = 14.
- P(red) = 4/14 = 2/7.
- Answer: P(red) = 2/7
A bag has 2 red, 8 blue and 3 green counters. One is picked at random. Find P(red) and P(not red).
- Total counters = 13.
- P(red) = 2/13 = 2/13.
- P(not red) = 1 − 2/13 = 11/13.
- Answer: P(red) = 2/13, P(not red) = 11/13
A bag has 5 red and 5 blue counters. Two are picked with replacement. Find P(both red).
- P(red) = 5/10 each time.
- Independent, so multiply: 5/10 × 5/10 = 1/4.
- Answer: 1/4
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Writes probability as a ratio like 3:5.
Correction: Use a fraction, decimal or percentage.
Adds probabilities for 'and' events.
Correction: 'And' means multiply when events are independent.
Teacher tips
- · Run real experiments with dice and compare to theory.
Parent tips
- · Talk about the chance of rain from the forecast.
Real-life applications
- · Weather forecasts, games, insurance.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
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- What should a learner already know before this?
- Start with Introducing Relative Frequency Essentials, Equally Likely Outcomes. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Introducing Relative Frequency Techniques?
- Move on to Introducing Relative Frequency Word Problems, Introducing Relative Frequency Common Errors, Working with Relative Frequency, Relative Frequency in Context, which build directly on this idea.
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