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Year 8 Mathematics · Probability and sample spaces

Name: ______________________

Date: ____________

1. What is the sample space when a coin is flipped?
- ☐ (a) {heads}
- ☐ (b) {heads, tails}
- ☐ (c) {1, 2}
- ☐ (d) {heads, tails, edge}
2. What is the probability of rolling a 5 on a fair six-sided die?
- ☐ (a) 15
- ☐ (b) 56
- ☐ (c) 16
- ☐ (d) 12
3. When a fair die is rolled, which event is most likely?
- ☐ (a) Rolling a 6
- ☐ (b) Rolling an even number
- ☐ (c) Rolling a number less than 3
- ☐ (d) Rolling a 7
4. A bag holds 3 red, 5 blue and 2 yellow marbles. One marble is taken without looking. What is P(blue)?
- ☐ (a) 12
- ☐ (b) 53
- ☐ (c) 15
- ☐ (d) 310
5. A spinner has 10 equal sections numbered 1 to 10. What is the probability of spinning a number greater than 7? Give your answer as a fraction.
6. What is the probability of NOT rolling a 2 on a fair six-sided die? Give your answer as a fraction.
7. A coin is flipped 40 times and lands on heads 18 times. What is the relative frequency of heads? Give a fraction in simplest form.
8. A bag has 4 green and 6 white counters. A counter is drawn and put back, 50 times. About how many times would you expect a green counter?

Answer sheet

1. {heads, tails} — A coin has two possible outcomes: heads and tails.
2. 16 — There is 1 favourable outcome (5) out of 6 equally likely outcomes.
3. Rolling an even number — P(6) = 16, P(even) = 36, P(less than 3) = 26 and P(7) = 0. Rolling an even number is most likely.
4. 12 — There are 10 marbles and 5 are blue: 510 = 12.
5. 3/10 — The numbers greater than 7 are 8, 9 and 10 — that is 3 outcomes out of 10.
6. 5/6 — P(2) = 16, so P(not 2) = 1 − 16 = 56. (The outcomes 1, 3, 4, 5 and 6 are favourable.)
7. 9/20 — Relative frequency = 1840 = 920 = 0.45.
8. 20 — P(green) = 410 = 0.4, and 0.4 × 50 = 20.