Expected outcomes and fairness worksheet — GCSE Foundation

1.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.

2.A grower knows that the probability that one of their seeds germinates is 0.6. The grower wants to expect 300 of the seeds to germinate. Work out how many seeds the grower should plant.

3.At a fête, a game costs £3 to play. The probability of winning is 0.1, and each win pays out £20. 150 people play the game. Work out the fête's expected profit from the game.

4.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.

5.On a Saturday, 2,000 customers go through the tills at a supermarket. The probability that a customer buys a reusable bag is 0.08. Work out how many customers you would expect to buy a reusable bag.

6.A raffle sells 400 tickets at 50p each. There is one prize of £45. Aisha buys 8 tickets. Work out how much money Aisha should expect to lose from playing, giving your answer in pounds.

7.A sorting office processes 2,000 letters addressed to one postcode area in a week. The probability that a letter is a bill is 0.15. Work out how many of the letters you would expect to be bills.

8.A game uses a fair spinner with 5 equal sections numbered 1 to 5. A player wins £12 if the spinner lands on 5, and wins nothing otherwise. It costs £2 to play. The game is played 250 times. Work out the expected profit for the players, in total, over the 250 games.

9.A spinner is divided into sectors of 144°, 90° and 126°, coloured purple, orange and grey in that order. The spinner is spun 300 times. Work out how many times you would expect it to land on purple.

10.A fair spinner has 6 equal sections, and 2 of the sections are coloured purple. The spinner is spun 180 times. Work out how many times you would expect it to land on purple.

11.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.

12.A spinner is divided into sectors of 180°, 120° and 60°, coloured red, blue and green in that order. The spinner is spun 60 times. Work out how many times you would expect it to land on green.

13.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.

14.An archer hits the bullseye with probability 0.24 on any one shot. She wants to know how many shots she must take to expect to hit the bullseye 12 times. Work out how many shots this is.

15.A charity fundraiser runs a game using a spinner with 5 equal sections numbered 1 to 5. A player wins a £4 prize if the spinner lands on 5, and wins nothing otherwise. It costs £1 to play, and the game is played 100 times during the fundraiser. Decide which statement correctly describes the game.