Probability worksheet — GCSE Foundation

1.A bag contains 2 white counters and 8 black counters. One counter is taken at random from the bag. Work out the probability that the counter is not black.

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

3.A charity bake sale tracked 240 items sold using a frequency tree. The first branch splits sales into 150 cake sales and 90 biscuit sales. Of the cake sales, 100 were bought by adults and the rest by children. Of the biscuit sales, 54 were bought by children. Each item sold for £1.20. Work out the total amount of money raised from sales to children.

4.A six-sided dice is rolled 12 times. It lands on a six 4 times. Erin says that the dice must be biased. Which of these is the best comment on Erin's statement?

5.At a leisure centre, 50 members are asked which activities they do. 32 do yoga, 24 do pilates, and 11 do both. Work out how many members do yoga only, and not pilates.

6.Bag A contains 3 red balls and 2 blue balls. Bag B contains 1 red ball and 3 blue balls. One ball is taken at random from each bag. Work out the probability that both balls are red.

7.A four-colour spinner (red, blue, green, yellow) is spun repeatedly, and the relative frequency of landing on green is recorded as the number of spins increases: after 20 spins it is 0.350; after 200 spins it is 0.290; after 2000 spins it is 0.251. Using the result from 2000 spins as the best estimate of the probability, work out the number of times the spinner would be expected to land on green in a further 3000 spins.

8.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.

9.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.

10.Ellie drops a bottle top and records whether it lands open end up. In her first 20 drops it lands open end up 13 times. She carries on, and after 200 drops in total it has landed open end up 84 times. Work out the best estimate of the probability that the bottle top lands open end up.

11.A box contains cards labelled 1, 2 and 3. A card is drawn at random and its number noted, then it is put back. A second card is then drawn at random. Every outcome is listed as an ordered pair, such as (1, 2). Work out how many of the outcomes in the full list have both numbers the same.

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.The universal set is {1, 2, 3, ..., 15}. A = {multiples of 3}. Work out n(A′), the number of elements not in A.

14.Two fair five-sided dice, numbered 1 to 5, are rolled. Work out the probability that the two scores differ by at least 2.

15.A phone network sends automatic text alerts to customers. On average, 1,500 alerts are sent each day, and the probability that a customer replies 'STOP' to an alert is 0.18. Work out how many replies of 'STOP' the network should expect over a 30-day month.