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S3 Maths: Basic Probability (Paper 3 (challenge))
Tutor Prep Guide · Sample space, favourable outcomes, complement, mutually exclusive and independent events, from dice, coins and drawing balls to expected counts
S3 Maths: Basic Probability (Paper 3 (challenge))
Paper 3 (challenge): ten questions on basic probability, with answers and one line notes.
Direct answers Level: S3 maths; format: probability questions on sample space, favourable outcomes, complement and independent events.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S3 Maths: Basic Probability |
| Level | S3 |
02 Questions (10 items)
- FoundationA bag holds 4 red balls and 6 blue balls. Two balls are drawn at random without replacement. Find the probability that both are red.
- FoundationTwo fair dice are thrown together. Find the probability that the total is exactly 8.
- FoundationA family has three children, with boys and girls equally likely. Find the probability of at least one boy.
- IntermediateTwo cards are drawn at random from a pack of 52 without replacement. Find the probability that both are hearts.
- IntermediateA bag holds 3 white balls and 2 black balls. Two balls are drawn without replacement. Given that the first is white, find the probability that the second is also white.
- IntermediateA fair die is rolled three times. Find the probability of at least one 6.
- ChallengeEvents A and B are independent with P(A) = 0.4 and P(B) = 0.5. Find P(A and B).
- ChallengeA raffle has 1000 tickets and 5 of them win. A person buys 3 tickets. Find the expected number of winning tickets.
- ChallengeA bag holds 5 red balls and 3 blue balls. Two balls are drawn without replacement. Find the probability that they differ in colour.
- Error redoError clinic: a student multiplies 4/10 by 4/10 to get 0.16 for two red balls drawn without replacement. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 2/15 | The first draw is red with probability 4/10, then 3 reds remain among 9 balls, so the product is 2/15. |
| 2 | 5/36 | Five ordered pairs add to 8, namely 2 and 6, 3 and 5, 4 and 4, 5 and 3, 6 and 2. |
| 3 | 7/8 | All three being girls has probability 1/8, so the complement gives 7/8. |
| 4 | 1/17 | The first heart has probability 13/52 and the second 12/51, giving 156/2652 which is 1/17. |
| 5 | 1/2 | After one white ball leaves, 4 balls remain and 2 of them are white, so the probability is 2/4. |
| 6 | 91/216 | No 6 at all has probability 125/216, so the complement gives 91/216. |
| 7 | 0.2 | For independent events the joint probability is the product, so 0.4 times 0.5 gives 0.2. |
| 8 | 0.015 | Each ticket wins with probability 5/1000, and multiplying by 3 gives 15/1000, that is 0.015. |
| 9 | 15/28 | Red then blue gives 5/8 times 3/7 and blue then red gives 3/8 times 5/7, adding to 15/28. |
| 10 | 2/15 | Without replacement the second denominator drops by one, so 4/10 times 3/9 gives 12/90, that is 2/15. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Write down the size of the sample space first, then count the favourable outcomes and divide. For at least or not, use the complement; for drawing without replacement, reduce the denominator.Tutor Registration →
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