Probability worksheet — GCSE Foundation

1.Each turn of a game ends in a win, a draw or a loss, and no turn can end in more than one of these. The probability of a win is 1/4 and the probability of a draw is 1/3. Work out the probability of a loss.

2.A bag is known to contain red, blue and green counters in equal numbers, so the theoretical probability of taking each colour is 1/3. In 90 trials with replacement, red was taken 38 times, blue was taken 26 times and green was taken 26 times. Which colour is over-represented compared with its theoretical probability?

3.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.

4.The probability that a seed fails to germinate is 1/5. Three seeds are planted independently. Work out the probability that at least one of the three seeds germinates.

5.180 gardeners at an allotment were asked whether they grow vegetables organically. 100 of the gardeners are on the north plots. 64 of the north-plot gardeners grow organically. 30 of the south-plot gardeners do not grow organically. Work out how many south-plot gardeners grow organically.

6.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.

7.The probability that the Hughes family go away during the summer holidays is 3/7. Work out the probability that they do not go away during the summer holidays.

8.A small pack contains 5 cards, numbered 1 to 5. One card is drawn at random from the pack, and a fair coin is flipped. Every outcome is listed as a pair, such as (3, H). Work out how many equally likely outcomes there are in total.

9.In Manchester the probability of rain on any day in November is taken to be 0.3, and whether it rains on one day is independent of whether it rains on the next. Work out the probability that it rains on both the 10th and the 11th of November.

10.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.

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.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.

13.The probability that a machine completes a task successfully is 0.85. Work out the probability that the machine does not complete the task successfully.

14.The probability that Oliver's train is delayed on any morning is 0.3. Work out the probability that his train is not delayed.

15.Bag A contains 3 red balls and 2 blue balls. Bag B contains 1 red ball and 3 blue balls. One ball is taken at random from each bag. Work out the probability that both balls are red.