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S3 Maths: Basic Probability (Paper 2 (intermediate))
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 2 (intermediate))
Paper 2 (intermediate): 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)
- FoundationTwo fair dice are thrown together. Find the probability that the total is at least 10.
- FoundationA bag holds 4 red balls and 6 blue balls. One ball is drawn at random. Find the probability that it is not red.
- FoundationFive per cent of the parts from a factory are defective. Find the expected number of defective parts in a random sample of 200.
- IntermediateTwo fair dice are thrown together. Find the probability that the total is even.
- IntermediateA bag holds 3 red balls and 5 green balls. A ball is drawn and replaced, then drawn again. Find the probability that both draws are green.
- IntermediateA fair spinner has eight equal sectors numbered 1 to 8. Find the probability of getting a prime number.
- ChallengeIn a class of 40 students, 12 wear glasses. One student is chosen at random. Find the probability that the student wears glasses.
- ChallengeEvents A and B are mutually exclusive with P(A) = 0.28 and P(B) = 0.45. Find P(A or B).
- ChallengeA fair die is rolled twice. Find the probability that both rolls show a 6.
- Error redoError clinic: for two green draws with replacement a student adds 5/8 and 5/8 to get 10/8. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1/6 | The totals 10, 11 and 12 come from 3, 2 and 1 pairs, giving 6 out of 36, which is 1/6. |
| 2 | 3/5 | Not red means one of the 6 blue balls, so 6/10 gives 3/5, which also equals 1 minus 2/5. |
| 3 | 10 | The expected count is the probability times the number of trials, so 0.05 times 200 gives 10. |
| 4 | 1/2 | The total is even when both dice are odd or both are even, which covers 18 of the 36 pairs. |
| 5 | 25/64 | With replacement the chance of green stays 5/8 each time, and multiplying gives 25/64. |
| 6 | 1/2 | The primes from 1 to 8 are 2, 3, 5 and 7, so 4 out of 8 gives 1/2. |
| 7 | 3/10 | There are 12 favourable students out of 40, and 12/40 simplifies to 3/10. |
| 8 | 0.73 | Mutually exclusive events cannot occur together, so the probabilities simply add to 0.73. |
| 9 | 1/36 | The two rolls are independent, so 1/6 times 1/6 gives 1/36. |
| 10 | 25/64 | The draws are independent, so the probabilities multiply rather than add, giving 25/64. |
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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