Printable · GCSE Foundation · ages 14-16
Expected outcomes and fairness worksheet — GCSE Foundation
Fifteen questions on "expected outcomes and fairness" — DfE statement P2. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
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Expected outcomes and fairness worksheet — GCSE Foundation
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- 1.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.
- 2.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.
- 3.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.
- 4.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.
- 5.A raffle at a school fair sells 500 tickets. Mia buys 25 of the tickets. One ticket is drawn at random to win the prize. Work out the probability that Mia wins the raffle. Give your answer as a fraction in its simplest form.
- 6.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.
- 7.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.
- 8.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.
- 9.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.
- 10.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.
- 11.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.
- 12.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.
- 13.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.
- 14.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.
- 15.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.
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