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S4 Maths: Probability and Statistics (Paper 3 (challenge))
S4 Maths: Probability and Statistics (Paper 3 (challenge))
Paper 3 (challenge): 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 7 or 11?
- FoundationA whole number from 1 to 10 is chosen at random. What is the probability that it is divisible by 2 or by 3?
- FoundationA and B are mutually exclusive with P(A) = 0.4 and P(B) = 0.5. Find the probability of A or B.
- IntermediateA bag holds three red and two white balls. Two are drawn without replacement. What is the probability that both are red?
- IntermediateThree dice are rolled. What is the probability that all three show 6?
- IntermediateFor the data 12, 15, 15, 18, 20, what are the median and the mean?
- ChallengeA bag holds five red and three blue balls. Two are drawn without replacement. What is the probability of at least one red ball?
- ChallengeA and B are independent with P(A and B) = 0.12 and P(A) = 0.4. Find P(B).
- ChallengeTwo dice are rolled. What is the probability that the product of the two numbers is 12?
- Error redoA student treats drawing two balls without replacement as drawing with replacement. Where does the error lie?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 8/36, about 0.222 | Six outcomes give seven and two give eleven. |
| 2 | 0.7 | Five even numbers plus three multiples of three, less the shared 6, gives seven. |
| 3 | 0.9 | Mutually exclusive events cannot overlap, so the probabilities simply add. |
| 4 | 0.3 | Three ways to choose two red balls out of ten ways to choose any two. |
| 5 | 1/216, about 0.005 | Each die gives one sixth, and the three independent results multiply. |
| 6 | Median 15, mean 16. | The middle value of the sorted list is 15, and eighty divided by five is 16. |
| 7 | About 0.893 | By complements, only three of the twenty-eight pairs are both blue. |
| 8 | 0.3 | The product rule for independent events gives 0.12 divided by 0.4. |
| 9 | 4/36, about 0.111 | The pairs 2 and 6, 6 and 2, 3 and 4, 4 and 3 give a product of twelve. |
| 10 | Without replacement the denominator for the second draw is one less, so using the full denominator makes the answer too large. | For five red and three blue, both blue is three over twenty-eight without replacement but nine over sixty-four with replacement. |
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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