Probability worksheet — GCSE Foundation

1.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.

2.A council surveyed 140 households about recycling. 85 of the households are in Zone A. 52 of the Zone A households recycle glass. 21 of the Zone B households do not recycle glass. Work out the probability that a household, chosen at random from the 140, recycles glass. Give your answer as a fraction in its simplest form.

3.A bag contains counters that are red, blue or green only. The probability that a counter taken at random is not red is 0.8. The bag contains 25 counters in total. Work out how many of the counters are red.

4.Kwame flips a fair coin three times and writes down what it lands on each time. Work out the probability that it lands on heads all three times.

5.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.

6.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.

7.120 members of a sports club were asked whether they play football or netball; each member plays exactly one of the two sports. 70 of the members are male. 45 of the male members play football. 38 of the female members play netball. Work out how many female members play football.

8.The probability that it rains in Manchester tomorrow is 1/12. Work out the probability that it does not rain in Manchester tomorrow.

9.At a summer fair, the probability of winning at the hoopla stall is 6/10 and the probability of winning at the coconut shy is 2/10. Work out how many times as likely a player is to win at the hoopla stall as at the coconut shy.

10.A fair six-sided dice is rolled once. Write down the probability that the score is an even number.

11.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.

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

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

14.Two games at a school fete are played independently. The probability of winning game X is 3/8. The probability of winning game Y is 0.4. Which statement correctly compares the two games?

15.Harry plays a game in which he flips a fair coin and rolls an ordinary fair dice. He wins a prize only if the coin shows heads and the dice shows a 6. Work out the probability that Harry wins a prize.