Probability worksheet — GCSE Higher

1.An ordinary fair dice is rolled once. Set A is the set of even scores and set B is the set of scores greater than 4. Work out the probability that the score rolled is in set A or in set B or in both.

2.A red dice and a blue dice are rolled. Both dice are ordinary and fair. Work out the probability of getting a 1 on the red dice and a 2 on the blue dice.

3.In a year group of 60 pupils, 25 play football, 18 play tennis and 8 play both football and tennis. A pupil who plays football or tennis or both is picked at random. Work out the probability that this pupil plays both sports.

4.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.

5.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.

6.Two fair four-sided dice, numbered 1 to 4, are rolled and the two scores are added together. Work out the probability that the total is 5.

7.Two ordinary fair dice are rolled. Work out the probability that the difference between the two scores is 1.

8.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.

9.180 gardeners at an allotment were asked whether they grow vegetables organically. 100 of the gardeners are on the north plots. 64 of the north-plot gardeners grow organically. 30 of the south-plot gardeners do not grow organically. Work out how many south-plot gardeners grow organically.

10.A pupil must choose 2 different subjects at random from these five: maths, physics, biology, chemistry and history. Work out the probability that the two subjects chosen are maths and biology.

11.Grace rolls two ordinary fair dice at the same time and works out the total of the two scores. Work out the probability that the total is greater than 10.

12.The probability that Kofi passes his driving test on any attempt is 0.6, and each attempt is independent of the others. Work out the probability that he fails both his first two attempts.

13.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.

14.A bag contains 3 yellow counters and 2 green counters. Sophie takes one counter at random and does not put it back. She then takes a second counter at random. Work out the probability that the first counter is yellow and the second is green.

15.A two-way table records 200 members of a gym. 80 of the members are women and the rest are men. 60 of the women attend yoga classes. Work out the percentage of the women who attend yoga classes.