Probability worksheet — GCSE Foundation

1.On the probability scale from 0 to 1, which word best describes an event with probability 0.9?

2.80 people are asked whether they drink tea and whether they drink coffee, and the results are recorded on a frequency tree. The first pair of branches splits the 80 people into 50 tea drinkers and 30 non-tea-drinkers. Of the 50 tea drinkers, 32 also drink coffee. Of the 30 non-tea-drinkers, 6 drink coffee. Work out n(T ∩ C), the number of people who drink both tea and coffee.

3.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.

4.A fair six-sided dice is rolled once. Write down the probability of rolling a 6.

5.A charity raffle sells 250 tickets. A group of friends buy 40 of the tickets between them. Three prizes are awarded, each to a different randomly drawn ticket, and no ticket can win more than one prize. Work out the expected number of prizes won by the group. Give your answer as a fraction in its simplest form.

6.A pupil must choose 2 different subjects at random from these five: maths, physics, biology, chemistry and history. Work out the probability that the two subjects chosen are maths and biology.

7.In a survey of 45 students, 22 said they like reading, 18 said they like gaming, and 6 said they like both. Work out how many students like exactly one of reading or gaming.

8.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.

9.Harry plays a game in which he flips a fair coin and rolls an ordinary fair dice. He wins a prize only if the coin shows heads and the dice shows a 6. Work out the probability that Harry wins a prize.

10.Grace rolls two ordinary fair dice at the same time and works out the total of the two scores. Work out the probability that the total is greater than 10.

11.Four students each drop a drawing pin repeatedly to estimate the probability that it lands point-up. Freya makes 20 drops, Malik makes 50 drops, Priya makes 200 drops and Tom makes 80 drops. Which student's relative frequency is likely to give the best estimate of the true probability?

12.In a class of 32 pupils, 19 study geography and 15 study history. 8 study both subjects. Work out n(G ∪ H), the number of pupils who study geography or history or both.

13.At a quiz night, each team's result is a win, a draw or a loss, and no team can have more than one of these results. The probability that a team wins is 42% and the probability that a team draws is 18.5%. Work out the probability, as a percentage, that a team does not win and does not draw.

14.The probability that a component is faulty is 1/10. Two components are tested independently. Work out the probability that at least one of the two components is faulty.

15.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?