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S3 Maths: Basic Probability (Paper 1 (basics))
Tutor Prep Guide · Sample space, favourable outcomes, complement, mutually exclusive and independent events, from dice, coins and drawing balls to expected counts
S3 Maths: Basic Probability (Paper 1 (basics))
Paper 1 (basics): ten questions on basic probability, with answers and one line notes.
Direct answers Level: S3 maths; format: probability questions on sample space, favourable outcomes, complement and independent events.
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: S3 Maths: Basic Probability |
| Level | S3 |
02 Questions (10 items)
- FoundationA fair die is rolled once. Find the probability of getting a 4.
- FoundationA fair die is rolled once. Find the probability of getting an even number.
- FoundationA bag holds 4 red balls and 6 blue balls. One ball is drawn at random. Find the probability that it is red.
- IntermediateTwo fair coins are tossed together. Find the probability that both show heads.
- IntermediateOne card is drawn at random from a standard pack of 52. Find the probability that it is a heart.
- IntermediateA fair die is rolled once. Find the probability of getting a number greater than 4.
- ChallengeTwo fair dice are thrown together. Find the probability that the total is exactly 7.
- ChallengeA whole number from 1 to 20 is chosen at random. Find the probability that it is a multiple of 3.
- ChallengeThe probability that an event happens is 0.35. Find the probability that it does not happen.
- Error redoError clinic: a student gives 1/6 for the probability that a die does not show 6. 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 of them is a 4. |
| 2 | 1/2 | There are three even numbers, 2, 4 and 6, so 3 out of 6 simplifies to 1/2. |
| 3 | 2/5 | There are 10 balls in total and 4 of them are red, so 4/10 simplifies to 2/5. |
| 4 | 1/4 | The sample space has four outcomes, heads-heads, heads-tails, tails-heads and tails-tails, and only one fits. |
| 5 | 1/4 | There are 13 hearts out of 52 cards, and 13/52 simplifies to 1/4. |
| 6 | 1/3 | Only 5 and 6 are greater than 4, so 2/6 simplifies to 1/3. |
| 7 | 1/6 | Six of the 36 equally likely pairs add to 7, and 6/36 simplifies to 1/6. |
| 8 | 3/10 | The multiples of 3 are 3, 6, 9, 12, 15 and 18, so 6 out of 20 simplifies to 3/10. |
| 9 | 0.65 | The probabilities of all outcomes add to 1, so 1 minus 0.35 gives 0.65. |
| 10 | 5/6 | Not getting a 6 covers the other five outcomes, so the answer is 5/6; the student swapped the two counts. |
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.
Write down the size of the sample space first, then count the favourable outcomes and divide. For at least or not, use the complement; for drawing without replacement, reduce the denominator.Tutor Registration →
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