Probability worksheet — GCSE Foundation

1.A fair six-sided dice is rolled once. Work out the probability that the score is an odd number. Give your answer as a decimal.

2.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.

3.The probability that Leo wakes up before his alarm is 0.35. The probability that his younger sister wakes up before her alarm, independently of Leo, is 0.28. Work out the probability that neither of them wakes up before their alarm.

4.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.

5.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.

6.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.

7.Two pupils each flip the same coin to estimate the probability of heads. Leah flips it 40 times and gets 24 heads. Ben flips it 60 times and gets 33 heads. By combining both pupils' results, work out the relative frequency of heads, giving your answer as a fraction in its simplest form.

8.At a fun run, each runner finishes, retires or is disqualified, and cannot do more than one of these. The probability that a runner finishes is 68.5% and the probability that a runner retires is 24.75%. Work out the probability, as a percentage, that a runner is disqualified.

9.A clinic recorded 300 booked appointments using a frequency tree. The first branch splits them into 210 adult appointments and the rest child appointments. Of the adult appointments, 189 were attended and the rest were missed. Of the child appointments, 81 were attended. Work out the probability that a booked appointment, chosen at random from the 300, was missed. Give your answer as a fraction in its simplest form.

10.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.

11.A biased spinner is spun 40 times and lands on red 16 times. It is then spun a further 60 times and lands on red 21 times. Work out the best estimate of the probability that the spinner lands on red, using the results of all 100 spins together.

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.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.

14.A library recorded loans for 250 books over a week, using a frequency tree. The first branch splits the books into 160 fiction and 90 non-fiction. Of the fiction books, 112 were returned on time and the rest were returned late. All the non-fiction books were returned on time. Work out the probability that a book, chosen at random from the 250, was returned late. Give your answer as a fraction in its simplest form.

15.A two-way table records 200 members of a gym. 80 of the members are women and the rest are men. 60 of the women attend yoga classes. Work out the percentage of the women who attend yoga classes.