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S3 Maths: Basic Probability (Paper 4 (error clinic))
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 4 (error clinic))
Paper 4 (error clinic): 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)
- FoundationError clinic: a student obtains 1.4 as the probability of an event. What is wrong?
- FoundationTwo fair coins are tossed together. Find the probability of getting one head and one tail.
- FoundationA bag holds 2 red balls and 3 blue balls. One ball is drawn at random. Find the probability that it is blue.
- IntermediateError clinic: a student writes 2/12 for the probability of rolling a 2 or a 5. What is correct?
- IntermediateA bag holds 3 red balls and 5 green balls. Two balls are drawn without replacement. Find the probability that both are green.
- IntermediateWhat is the probability of an impossible event?
- ChallengeError clinic: a student writes P(not A) as 1 plus P(A). If P(A) = 0.3, what is the correct probability?
- ChallengeOne card is drawn at random from a pack of 52. Find the probability that it is not a heart.
- ChallengeTwo fair dice are thrown together. Find the probability that the total is exactly 2.
- Error redoError clinic: a student claims that after five sixes in a row the next roll is less likely to be a 6. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | A probability must lie between 0 and 1, so 1.4 is impossible | Probability is favourable outcomes divided by the sample space, and the numerator cannot exceed the denominator. |
| 2 | 1/2 | Both head then tail and tail then head count, so 2/4 gives 1/2; forgetting one order is a common error. |
| 3 | 3/5 | There are 3 blue balls among 5 in total, and 3/5 is already in simplest form. |
| 4 | 1/3 | The sample space is still six outcomes with two favourable ones, so 2/6 gives 1/3; the denominators are not added. |
| 5 | 5/14 | The first green ball has probability 5/8, then 4 of the remaining 7 are green, giving 20/56 which is 5/14. |
| 6 | 0 | An impossible event has no favourable outcome, and zero divided by the sample space is still zero. |
| 7 | 0.7 | The complement uses subtraction, so 1 minus 0.3 gives 0.7, while adding would exceed 1. |
| 8 | 3/4 | Not a heart covers the other three suits, that is 39 cards, and 39/52 simplifies to 3/4. |
| 9 | 1/36 | Only the pair 1 and 1 gives a total of 2, so it is one outcome out of 36. |
| 10 | Still 1/6 | Each roll is independent, so earlier results do not change the next roll and the probability stays 1/6. |
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 →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
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