Probability worksheet — GCSE Foundation

1.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.

2.A café offers 3 types of sandwich, cheese, ham and egg, and 4 types of drink, tea, coffee, juice and water. A customer chooses one sandwich and one drink at random. Work out the probability that the customer chooses egg and water.

3.A fair six-sided dice is rolled once. Work out the probability that the score is an odd number. Give your answer as a decimal.

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

5.A = {factors of 12} and B = {factors of 18}. Work out n(A ∩ B), the number of elements in both sets.

6.A bag contains 20 counters. 8 of the counters are red and 12 are blue. A counter is taken at random, its colour is recorded, and it is put back in the bag. This is done 150 times. Work out how many red counters you would expect to be recorded.

7.A fair six-sided dice is rolled 90 times. Work out how many more times you would expect it to land on a number less than 4 than on a 6.

8.In a game, Freddie says the probability of winning is 0.45, the probability of drawing is 0.3 and the probability of losing is 0.35, and that all three of his probabilities are correct. Which statement about Freddie's probabilities is correct?

9.A frequency tree records how 90 pupils travel to school and whether they were late. The first pair of branches splits the 90 pupils into 50 who walk and 40 who do not walk. On the walking branch, 6 were late and 44 were not. On the other branch, 10 were late and 30 were not. One of the 90 pupils is chosen at random. Work out the probability that the pupil walks to school and was late.

10.A fair spinner has 8 equal sections. 3 of the sections are red. The spinner is spun 240 times. Work out how many times you would expect it to land on red.

11.A bag contains 3 red counters, 2 blue counters and 2 green counters. One counter is taken at random from the bag. Work out the probability that the counter is red.

12.A machine produces bolts. In a sample of 250 bolts, 15 are faulty. Work out the relative frequency of a bolt being faulty, giving your answer as a fraction in its simplest form.

13.A survey asks 40 people whether they own a cat, a dog, both, or neither. 12 people own only a cat, 15 own only a dog, 5 own both, and 8 own neither. Work out the probability that a randomly chosen person owns a cat or a dog (or both). Give your answer as a fraction in its simplest form.

14.A drawer contains 4 red socks and 2 blue socks. Two socks are taken out at random, one after the other, without the first being put back. Work out the probability that both socks are the same colour.

15.A fair six-sided dice is rolled once. Write down the probability of rolling a 6.