Relative frequency and the probability scale worksheet — GCSE Foundation

1.A bag contains 3 red counters, 2 blue counters and 2 green counters. One counter is taken at random from the bag. Work out the probability that the counter is red.

2.A fair six-sided dice is rolled 150 times. The table shows how many times each number came up: 1 came up 22 times, 2 came up 27 times, 3 came up 24 times, 4 came up 34 times, 5 came up 21 times and 6 came up 22 times. The theoretical probability of each number is 1/6. Which number is most over-represented compared with its theoretical probability?

3.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?

4.A spinner is divided into 8 equal sections. 3 of the sections are red and the rest are not red. The spinner is spun once. Work out the probability that it does not land on red.

5.A fair six-sided dice is rolled once. Work out the probability that the score is greater than 4.

6.The probability that a pupil chosen at random has a nut allergy is 1/10. There are 30 pupils in a class. Work out how many of the 30 pupils would be expected to have a nut allergy.

7.A spinner is spun 50 times. It lands on green 18 times. Work out the relative frequency of landing on green.

8.A fair six-sided dice is rolled once. Write down the probability that the score is an even number.

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

10.One card is taken at random from an ordinary pack of 52 playing cards. 26 of the cards are red. Work out the probability that the card is red. Give your answer as a percentage.

11.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.

12.A market research company found that, out of 120 shoppers surveyed, 42 preferred paper bags to plastic bags. A supermarket expects 900 shoppers this week. Using this relative frequency, work out how many of the 900 shoppers would be expected to prefer paper bags.

13.The probability that a spinner lands on blue is 2/5. Write this probability as a percentage.

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

15.A machine produces bolts. In a sample of 250 bolts, 15 are faulty. Work out the relative frequency of a bolt being faulty, giving your answer as a fraction in its simplest form.