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S4 Maths: Probability and Statistics (Paper 2 (intermediate))
S4 Maths: Probability and Statistics (Paper 2 (intermediate))
Paper 2 (intermediate): ten questions on probability and statistics with answers and one-line notes.
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: S4 Maths: Probability and Statistics |
| Level | S4 |
02 Questions (10 items)
- FoundationTwo dice are rolled. What is the probability that the total is 12?
- FoundationFor the data 2, 4, 4, 6, 9, what are the mean and the mode?
- FoundationA coin is tossed twice. What is the probability of at least one head?
- IntermediateTwo dice are rolled. What is the probability that the total is 5?
- IntermediateOne card is drawn from a pack of 52. What is the probability of an ace or a king?
- IntermediateIn a class of 40, 12 wear glasses. Two students are drawn one after another without replacement. What is the probability that both wear glasses?
- ChallengeTwo dice are rolled. What is the probability that the total is 8 or 9?
- ChallengeA coin is tossed three times. What is the probability of exactly one head?
- ChallengeA box holds five balls numbered 1 to 5. Two are drawn without replacement. What is the probability that the sum of the numbers is even?
- Error redoA student believes that mutually exclusive events must be complementary. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1/36, about 0.028 | Only 6 and 6 works, which is one outcome out of thirty-six. |
| 2 | Mean 5, mode 4. | The total of twenty-five divided by five is 5, and 4 appears most often. |
| 3 | 0.75 | By complements, only one of the four outcomes has no head, so one minus one quarter. |
| 4 | 4/36, about 0.111 | Four of the thirty-six outcomes give a total of five. |
| 5 | 8/52, about 0.154 | Four aces and four kings make eight favourable cards out of fifty-two. |
| 6 | About 0.085 | Twelve out of forty, then eleven out of thirty-nine, multiplied together. |
| 7 | 0.25 | Five outcomes give eight and four give nine, which is nine out of thirty-six. |
| 8 | 0.375 | Three of the eight sequences have exactly one head. |
| 9 | 0.4 | Both odd or both even gives four favourable pairs out of the ten possible pairs. |
| 10 | Mutually exclusive only means the two cannot happen together, and they are complementary only when together they cover every outcome. | For instance, rolling a 1 and rolling a 2 are mutually exclusive but do not add up to one. |
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.
For probability questions, list the sample space first and count the total number of outcomes. For at least one, use the complement: one minus the probability of none. Check whether sampling is with or without replacement, because without replacement the denominator drops each time. Mutually exclusive means the events cannot happen together, while independent means the product rule holds, and the two ideas must not be mixed up. For statistics, sort the data before taking the median, and the mean is the total divided by the number of values.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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