Probability worksheet — GCSE Foundation

1.At a summer fair, the probability of winning at the hoopla stall is 6/10 and the probability of winning at the coconut shy is 2/10. Work out how many times as likely a player is to win at the hoopla stall as at the coconut shy.

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

3.Oliver flips three fair coins at the same time. Work out the probability that exactly two of the three coins land on heads.

4.A bag contains 2 white counters and 8 black counters. One counter is taken at random from the bag. Work out the probability that the counter is not black.

5.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.

6.Five raffle tickets numbered 1 to 5 are in a bag. Two tickets are drawn one after the other and the first is not put back. Work out the probability that ticket 1 is drawn first and ticket 2 is drawn second.

7.Two events are independent. The first has probability 2/5 and the second has probability 1/3. Work out the probability that both events happen.

8.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?

9.A spinner has three equal sections, coloured red, blue and green. It is spun twice, and each outcome is listed as an ordered pair of colours, such as (red, blue). Work out how many outcomes are in the full list.

10.A cinema sold 150 tickets for a Saturday screening. A frequency tree records the sales: 90 of the tickets were bought by adults and the rest by children. Of the adult tickets, 54 were for the 3D showing and the rest were for the standard showing. Work out how many adult tickets were for the standard showing.

11.Two fair four-sided dice, numbered 1 to 4, are rolled and the two scores are added together. Work out the probability that the total is 5.

12.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.

13.Amir has 3 different coloured pens, red, blue and green, and 2 different types of paper, lined and plain. He wants to choose one pen and one type of paper, and draws a grid to list every combination systematically. Work out how many combinations are in his grid.

14.At a gym, 70 members are asked whether they use the pool or the sauna. 38 use the pool, 30 use the sauna, and 12 use neither. Work out n(P ∩ S), the number of members who use both the pool and the sauna.

15.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.