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S4 Maths: Probability and Statistics (Paper 4 (error clinic))
S4 Maths: Probability and Statistics (Paper 4 (error clinic))
Paper 4 (error clinic): 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 getting 6?
- FoundationA bag holds two red and eight blue balls. One ball is drawn at random. What is the probability that it is red?
- FoundationGiven P(A) = 0.7, what is the probability of the complement of A?
- IntermediateA whole number from 1 to 12 is chosen at random. What is the probability that it is a multiple of 4?
- IntermediateTwo dice are rolled. What is the probability that the total is 2?
- IntermediateFive numbers have a mean of 12. A value of 24 is added. What is the new mean?
- ChallengeTwo dice are rolled. What is the probability that the two numbers are the same?
- ChallengeA coin is tossed four times. What is the probability of at least one tail?
- ChallengeA class of 40 has 25 girls and 15 boys. Two students are chosen at random. What is the probability of one boy and one girl?
- Error redoA student obtains the probability 1.3. Why must this answer be wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1/6, about 0.167 | Only one of the six faces shows six. |
| 2 | 0.2 | Two red out of ten balls gives one fifth. |
| 3 | 0.3 | One minus 0.7 gives 0.3, and the two probabilities always add to one. |
| 4 | 0.25 | The multiples 4, 8 and 12 are three of the twelve numbers. |
| 5 | 1/36, about 0.028 | Only 1 and 1 gives a total of two out of thirty-six outcomes. |
| 6 | 14 | The original total is sixty, plus twenty-four gives eighty-four over six. |
| 7 | 1/6, about 0.167 | The six doubles are 11, 22, 33, 44, 55 and 66. |
| 8 | 0.9375 | By complements, only one of the sixteen results has no tail at all. |
| 9 | About 0.481 | Twenty-five times fifteen favourable pairs out of seven hundred and eighty pairs. |
| 10 | Every probability lies between 0 and 1, so 1.3 is out of range and the working must be checked. | A value above one usually means too many favourable outcomes were counted or the denominator is not the whole sample space. |
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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