Expected outcomes and fairness worksheet — GCSE Foundation

1.A factory finds that the probability a randomly chosen light bulb is defective is 0.035. In a batch of 4,000 bulbs, work out how many bulbs you would expect to work correctly.

2.A fair six-sided dice is rolled 120 times. Work out how many of the rolls you would expect to give a score of 3 or more.

3.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.

4.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.

5.At a school fête, a tombola stall costs £1.50 to play. The probability of winning is 0.2, and the prize is worth £6. Work out the stall's expected profit, on average, from each game played.

6.Dice A is a fair six-sided dice. Dice B is biased so that P(6) = 0.3. Dice A is rolled 150 times and Dice B is rolled 150 times. Work out how many more sixes you would expect from Dice B than from Dice A.

7.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.

8.At a fun run, a raffle stall charges £1.50 per ticket. The probability that any one ticket wins a prize worth £8 is 0.12, and a losing ticket wins nothing. Nadia buys 25 tickets. Work out how much money Nadia should expect to lose in total.

9.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.

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 fair six-sided dice is rolled 90 times. Work out how many more times you would expect it to land on a number less than 4 than on a 6.

12.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.

13.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.

14.At a fair, a game costs £2 to play. The probability of winning the game is 0.15, and each win pays out £10. Amir plays the game 200 times. Work out how much money Amir should expect to lose in total.

15.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.