Free Grade 3 Introducing Sample Space Diagrams Lesson Plans
Free Grade 3 lesson plans for Introducing Sample Space Diagrams: 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing sample space diagrams
Identify introducing sample space diagrams accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing sample space diagrams
Explain introducing sample space diagrams accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing sample space diagrams
Calculate introducing sample space diagrams accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing sample space diagrams
Compare introducing sample space diagrams 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 Sample Space Diagrams 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 3 red, 5 blue and 4 green counters. One is picked at random. Find P(red).[1]
- 2.A bag has 6 red, 8 blue and 1 green counters. One is picked at random. Find P(red).[1]
- 3.A bag has 5 red, 4 blue and 5 green counters. One is picked at random. Find P(red).[1]
- 4.A bag has 1 red, 4 blue and 0 green counters. One is picked at random. Find P(red).[1]
- 5.A bag has 5 red, 7 blue and 1 green counters. One is picked at random. Find P(red) and P(not red).[2]
- 6.A bag has 3 red, 3 blue and 4 green counters. One is picked at random. Find P(red) and P(not red).[2]
- 7.A bag has 4 red, 5 blue and 0 green counters. One is picked at random. Find P(red) and P(not red).[2]
- 8.A bag has 6 red, 8 blue and 5 green counters. One is picked at random. Find P(red) and P(not red).[2]
- 9.A bag has 3 red and 2 blue counters. Two are picked with replacement. Find P(both red).[3]
- 10.A bag has 6 red and 1 blue counters. Two are picked with replacement. Find P(both red).[3]
- 11.A bag has 3 red and 6 blue counters. Two are picked with replacement. Find P(both red).[3]
- 12.A bag has 4 red and 3 blue counters. Two are picked with replacement. Find P(both red).[3]
Show answers and working
1. P(red) = 1/4
Total counters = 12. P(red) = 3/12 = 1/4.
2. P(red) = 2/5
Total counters = 15. P(red) = 6/15 = 2/5.
3. P(red) = 5/14
Total counters = 14. P(red) = 5/14 = 5/14.
4. P(red) = 1/5
Total counters = 5. P(red) = 1/5 = 1/5.
5. P(red) = 5/13, P(not red) = 8/13
Total counters = 13. P(red) = 5/13 = 5/13. P(not red) = 1 − 5/13 = 8/13.
6. P(red) = 3/10, P(not red) = 7/10
Total counters = 10. P(red) = 3/10 = 3/10. P(not red) = 1 − 3/10 = 7/10.
7. P(red) = 4/9, P(not red) = 5/9
Total counters = 9. P(red) = 4/9 = 4/9. P(not red) = 1 − 4/9 = 5/9.
8. P(red) = 6/19, P(not red) = 13/19
Total counters = 19. P(red) = 6/19 = 6/19. P(not red) = 1 − 6/19 = 13/19.
9. 9/25
P(red) = 3/5 each time. Independent, so multiply: 3/5 × 3/5 = 9/25.
10. 36/49
P(red) = 6/7 each time. Independent, so multiply: 6/7 × 6/7 = 36/49.
11. 1/9
P(red) = 3/9 each time. Independent, so multiply: 3/9 × 3/9 = 1/9.
12. 16/49
P(red) = 4/7 each time. Independent, so multiply: 4/7 × 4/7 = 16/49.
Worked examples
A bag has 1 red, 1 blue and 5 green counters. One is picked at random. Find P(red).
- Total counters = 7.
- P(red) = 1/7 = 1/7.
- Answer: P(red) = 1/7
A bag has 4 red, 4 blue and 2 green counters. One is picked at random. Find P(red) and P(not red).
- Total counters = 10.
- P(red) = 4/10 = 2/5.
- P(not red) = 1 − 2/5 = 3/5.
- Answer: P(red) = 2/5, P(not red) = 3/5
A bag has 8 red and 1 blue counters. Two are picked with replacement. Find P(both red).
- P(red) = 8/9 each time.
- Independent, so multiply: 8/9 × 8/9 = 64/81.
- Answer: 64/81
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
- Is this Grade 3 Introducing Sample Space Diagrams lesson plan really free?
- Yes. Every lesson plans on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Basic Probability. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan 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 Sample Space Diagrams?
- Move on to Working with Sample Space Diagrams, Sample Space Diagrams in Context, Tree Diagrams, Venn Diagrams, which build directly on this idea.
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