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S4 Maths: Probability and Statistics (Paper 1 (basics))
S4 Maths: Probability and Statistics (Paper 1 (basics))
Paper 1 (basics): 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)
- FoundationA fair die is rolled once. What is the probability of an even number?
- FoundationA bag holds three red and seven blue balls. One ball is drawn at random. What is the probability that it is red?
- FoundationGiven P(A) = 0.35, what is the probability of the complement of A?
- IntermediateTwo dice are rolled together. How many possible outcomes are there in total?
- IntermediateA whole number from 1 to 20 is chosen at random. What is the probability that it is a prime number?
- IntermediateOne card is drawn at random from a standard pack of 52. What is the probability that it is a heart?
- ChallengeTwo dice are rolled. What is the probability that the total is 7?
- ChallengeA coin is tossed three times. What is the probability of exactly two heads?
- ChallengeA whole number from 1 to 30 is chosen at random. What is the probability that it is a multiple of 3 or of 5?
- Error redoA student answers that the probability of getting 7 on one die is one sixth. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1/2, that is 0.5. | Three of the six outcomes, 2, 4 and 6, are even. |
| 2 | 0.3 | Three red out of ten balls in total gives three tenths. |
| 3 | 0.65 | The complement is one minus the probability, so one minus 0.35 is 0.65. |
| 4 | 36 | Six outcomes for the first die times six for the second gives thirty-six. |
| 5 | 0.4 | From 1 to 20 there are eight primes, namely 2, 3, 5, 7, 11, 13, 17 and 19. |
| 6 | 0.25 | There are thirteen hearts out of fifty-two cards, which is one quarter. |
| 7 | 1/6, about 0.167 | Six of the thirty-six outcomes give a total of seven. |
| 8 | 0.375 | Three of the eight equally likely sequences have exactly two heads. |
| 9 | 14/30, about 0.467 | Ten multiples of three plus six of five, minus the two counted twice, gives fourteen. |
| 10 | A die shows 1 to 6 only, so 7 is impossible and its probability is 0. | An impossible event has probability zero, while one sixth is the probability of each face that can appear. |
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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