Probability worksheet — GCSE Foundation

1.An ordinary fair dice is rolled twice. Work out the probability of getting at least one 5.

2.Two games are offered at a school fair, and every one of the 40 pupils in a class plays each game once. In Game A, the probability of winning a prize is 0.2 and the prize is worth £5. In Game B, the probability of winning a prize is 0.1 and the prize is worth £12. Work out which game gives a higher expected total value of prizes for the class, and by how much.

3.Spinner A is numbered 1 to 3 and Spinner B is numbered 1 to 5. Both spinners are spun once, and every outcome is listed as a pair, one number from each spinner. Work out how many equally likely outcomes there are in total.

4.Two fair coins are thrown together 400 times. Work out how many of the 400 throws you would expect to give one head and one tail.

5.A fair coin is flipped and a fair five-sided spinner, labelled 1 to 5, is spun. All the outcomes are listed as pairs, such as (H, 3). Work out the probability that the outcome is a tail and an odd number.

6.On the probability scale from 0 (impossible) to 1 (certain), evens is exactly halfway. An event is 3/10 more likely than evens. Work out the probability of that event, giving your answer as a decimal.

7.A fair coin is flipped three times. Work out the probability of getting at least one head.

8.In a board game Mia moves forward by the total of two ordinary fair dice. Work out the probability that her total is 7. Give your answer as a fraction in its simplest form.

9.Jack rolls two ordinary fair dice and adds the two scores together. Work out the probability that the total is 6.

10.Five raffle tickets numbered 1 to 5 are in a bag. Two tickets are drawn one after the other and the first is not put back. Work out the probability that ticket 1 is drawn first and ticket 2 is drawn second.

11.Two ordinary fair dice are rolled and the two scores are added together. Work out the probability that the total is a prime number.

12.A fair six-sided dice is rolled 300 times. Work out how many more times you would expect it to land on an even number than on a six.

13.The probability that a plant grown from a seed packet germinates is 7/10. Work out the probability that it does not germinate.

14.A bag is known to contain red, blue and green counters in equal numbers, so the theoretical probability of taking each colour is 1/3. In 90 trials with replacement, red was taken 38 times, blue was taken 26 times and green was taken 26 times. Which colour is over-represented compared with its theoretical probability?

15.A padlock code is formed by arranging three different digits chosen from 2, 3, 4 and 5, with no digit repeated. Work out how many different three-digit codes can be made.