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S6 Mathematics: Probability Practice Paper 4
S6 Mathematics: Probability Practice Paper 4
Set four closes with single events: a prime score, seven red and three white, a picture card and at least one head, then a total of eight, red or picture, same colour without replacement, a product of twelve and at least one red, ending with the error of adding independent events as if exclusive.
Quick answer 1/2, 7/10, 3/13, 3/4, 5/36, 8/13, 4/9, 1/9, 13/15 and 0.15.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | 25 minutes |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: S6 Mathematics: Probability – Tutor Lesson Plan |
| Level | S6 |
02 Questions (10 items)
- FoundationA fair die is rolled once. What is the probability of a prime score?
- FoundationA bag holds 7 red and 3 white balls. One ball is drawn at random. What is the probability it is red?
- FoundationOne card is drawn from a 52-card deck. What is the probability it is a picture card, J, Q or K?
- FoundationTwo fair coins are tossed. What is the probability of at least one head?
- IntermediateTwo fair dice are rolled. What is the probability that the total is 8?
- IntermediateOne card is drawn from 52. What is the probability it is red or a picture card?
- IntermediateA bag holds 4 red and 5 white balls. Two are drawn without replacement. What is the probability they match in colour?
- ChallengeTwo fair dice are rolled. What is the probability that the product of the scores is 12?
- ChallengeA bag holds 6 red and 4 blue balls. Two are drawn without replacement. What is the probability of at least one red?
- Error redoA and B are independent with P(A) = 0.3 and P(B) = 0.5. Find P(A and B).
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1/2 | The three outcomes 2, 3 and 5 qualify, so 3 out of 6 is one half. |
| 2 | 7/10 | Seven of the ten balls are red, so the probability is 7/10. |
| 3 | 3/13 | There are 12 picture cards, so 12 over 52 simplifies to 3/13. |
| 4 | 3/4 | Only TT fails, so 1 minus one quarter is three quarters. |
| 5 | 5/36 | Five of the 36 pairs total 8, so the probability is 5/36. |
| 6 | 8/13 | That is 26 plus 12 minus 6, giving 32 of 52, which simplifies to 8/13. |
| 7 | 4/9 | Add C(4,2) and C(5,2) over C(9,2), that is 16 over 36, giving 4/9. |
| 8 | 1/9 | Only the four pairs (2,6), (6,2), (3,4) and (4,3) work, so 4 over 36 is 1/9. |
| 9 | 13/15 | The complement is two blue balls, C(4,2) over C(10,2) equals 6 over 45, so 1 minus 2/15 is 13/15. |
| 10 | 0.15 | Independent events multiply, so 0.3 x 0.5 is 0.15; answering 0.8 wrongly adds them as exclusive. |
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.
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