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S4 Mathematics: Probability (Paper 2)
S4 Mathematics: Probability (Paper 2)
Ten original questions focus on two events happening together: one die and two dice give one sixth and one thirty-sixth, sums of seven, at least one head by complement, independent events multiplied, and red balls drawn with and without replacement giving nine twenty-fifths and three tenths. Two spinners and a passing pair at 0.72 follow, ending with the error of adding instead of multiplying for and.
Direct answer Decide first whether the events are independent, then multiply for independent events and add only when they are mutually exclusive.
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 fair die is rolled. Find the probability of getting a 6.
- FoundationTwo fair dice are rolled together. Find the probability that both show a 6.
- FoundationTwo fair dice are rolled. Find the probability that the total is 7.
- FoundationTwo fair coins are tossed. Find the probability of at least one head.
- IntermediateP(A) = 1/2 and P(B) = 1/3, with A and B independent. Find P(A and B).
- IntermediateA bag holds 3 red and 2 other balls. A ball is drawn, replaced, then drawn again. Find the probability that both are red.
- IntermediateFrom the same bag (3 red and 2 other balls) two balls are drawn without replacement. Find the probability that both are red.
- ChallengeSpinner A has faces 1 to 4 and spinner B has faces 1 to 6. Find the probability that both show the same number.
- ChallengeMing passes with probability 0.8 and Fun passes with probability 0.9, independently. Find the probability that at least one of them fails.
- Error redoError repair: A and B are independent with P(A) = 1/2 and P(B) = 1/4. A student answers three quarters for P(A and B). What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1/6 | All six outcomes are equally likely and only one is a six. |
| 2 | 1/36 | The dice are independent, so one sixth times one sixth. |
| 3 | 1/6 | There are six ways to make a sum of seven out of thirty-six outcomes. |
| 4 | 3/4 | Use the complement: both tails is one quarter, so the rest is three quarters. |
| 5 | 1/6 | For independent events the word and means multiply. |
| 6 | 9/25 | Replacing the ball keeps the draws independent, so square three fifths. |
| 7 | 3/10 | Without replacement the second draw has only four balls left, two of them red. |
| 8 | 1/6 | There are twenty-four equally likely pairs and only four match. |
| 9 | 0.28 (that is 7/25) | First find both passing as 0.72, then take the complement. |
| 10 | 1/8 | Three quarters is the addition used for or; independent events need multiplication for and. |
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.
