Relative frequency and the probability scale worksheet — GCSE Foundation

1.In a trial, a drawing pin was dropped 80 times and landed point-up 52 times. Assuming this relative frequency continues, work out how many times you would expect it to land point-up in 300 drops.

2.On a probability scale from 0 to 1, the points impossible (0), unlikely (0.25), evens (0.5) and certain (1) are marked. An event has a probability of 0.3. Between which two neighbouring marked points does 0.3 lie?

3.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?

4.Two games at a school fete are played independently. The probability of winning game X is 3/8. The probability of winning game Y is 0.4. Which statement correctly compares the two games?

5.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.

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

7.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.

8.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.

9.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?

10.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.

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

12.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.

13.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.

14.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.

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