Probability worksheet — GCSE Foundation

1.Two sets, A and B, sit inside a universal set. A region of a Venn diagram is described by the notation A ∩ B′. Work out which of these describes that region.

2.A fair spinner has 8 equal sections: 5 are red and 3 are blue. Freya spins it twice, and each spin is independent of the other. Work out the probability that she gets one red and one blue in the two spins, in either order.

3.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.

4.A bag contains 5 red counters and 3 blue counters. A counter is taken at random, its colour is noted, and it is put back in the bag before a second counter is taken at random. Work out the probability that both counters are the same colour.

5.A basketball player has a free-throw success probability of 0.75. She wants to expect to score 60 successful free throws. Work out how many free throws she needs to attempt.

6.Leo flips a fair coin twice. He makes a list of every possible result of the two flips, writing down what the first flip lands on and then what the second flip lands on. Work out how many of the results in his list contain at least one tail.

7.The probability that Ben catches his bus on time is 0.8. The probability that Freya catches her bus on time is 0.5. The two events are independent. Work out the probability that both Ben and Freya catch their bus on time.

8.Four bags each contain counters, some of which are winning counters. The probability of taking a winning counter is 5/12 from the red bag, 3/8 from the blue bag, 7/24 from the green bag and 1/3 from the yellow bag. Work out which bag has the smallest probability of giving a winning counter.

9.A bag contains 45 sweets. 18 of the sweets are lemon flavour and the rest are orange. A sweet is taken at random, its flavour is recorded, and it is put back in the bag. This is repeated 200 times. Work out how many times you would expect an orange sweet to be taken.

10.A fair spinner has 10 equal sections, numbered 1 to 10. The spinner is spun 150 times. Work out how many times you would expect it to land on a number greater than 7.

11.A leisure centre has 150 members. 80 of the members are male and the rest are female. Every member uses either the pool or the gym, but not both. 66 members use the pool, and 35 of those pool users are male. Work out how many female members use the gym.

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

13.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.

14.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.

15.A bag contains 5 red counters and 5 green counters. Three counters are taken out one at a time and are not put back. Work out the probability that all three counters are red.