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S4 Mathematics: Probability (Paper 1)
S4 Mathematics: Probability (Paper 1)
Ten original questions start from the classical definition of probability with balls in a bag, a prime on a die, a spinner above five and two coins, then use the complement for a dry day. Later items cover red balls with and without replacement, a heart from a pack, expected counts, the addition rule for mutually exclusive events, and repair the common error of using the wrong denominator.
Direct answer Write down the number of equally likely outcomes, count the favourable ones, divide and simplify.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 25 |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: S4 Mathematics: Probability |
| Level | Four basic, three advanced, two challenge and one error-repair item |
02 Questions (10 items)
- FoundationA bag holds 3 red, 5 blue and 2 green balls. One ball is drawn at random. Find the probability that it is red.
- FoundationA fair die is rolled once. Find the probability of getting a prime number.
- FoundationThe chance of rain is 0.35. Find the probability that it does not rain.
- FoundationA fair spinner has faces 1 to 8. Find the probability of a number greater than 5.
- IntermediateTwo fair coins are tossed together. Find the probability that both show tails.
- IntermediateA bag holds 4 red and 6 white balls. One ball is drawn. Give the probability of red as a fraction in lowest terms and as a decimal.
- IntermediateOne card is drawn from a standard pack of 52. Find the probability that it is a heart.
- ChallengeA fair die is rolled 60 times. Find the expected number of fives.
- ChallengeEvents A and B are mutually exclusive, with P(A) = 0.42 and P(B) = 0.35. Find P(A or B).
- Error redoError repair: a bag holds 2 red and 3 blue balls and a student answers two thirds for red. What is the correct answer?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3/10 (that is 0.3) | Probability is the favourable count divided by the total count, so 3 out of 10. |
| 2 | 1/2 | The primes among 1 to 6 are 2, 3 and 5, so the probability is 3 out of 6. |
| 3 | 0.65 | No rain is the complement of rain, so subtract 0.35 from 1. |
| 4 | 3/8 | Only 6, 7 and 8 are greater than 5, giving 3 out of 8. |
| 5 | 1/4 | The two coins are independent, so multiply one half by one half. |
| 6 | 2/5 (that is 0.4) | Four red out of ten balls simplifies to two fifths. |
| 7 | 1/4 | There are 13 hearts in the pack, so the probability is 13 out of 52. |
| 8 | 10 times | Expected count is the number of trials times the probability, so sixty times one sixth. |
| 9 | 0.77 | Mutually exclusive events cannot happen together, so add the two probabilities. |
| 10 | 2/5 | Two thirds divides by the blue balls; the denominator must be all five balls. |
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.
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.
