Relative frequency and the probability scale worksheet — GCSE Foundation

1.An ordinary pack of 52 playing cards contains 13 hearts. One card is taken at random from the pack. Work out the probability that the card is not a heart. Give your answer as a percentage.

2.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?

3.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?

4.Four bags each contain counters, some of which are winning counters. The probability of taking a winning counter is 5/12 from the red bag, 3/8 from the blue bag, 7/24 from the green bag and 1/3 from the yellow bag. Work out which bag has the smallest probability of giving a winning counter.

5.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?

6.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.

7.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.

8.On the probability scale from 0 (impossible) to 1 (certain), evens is exactly halfway. An event is 3/10 more likely than evens. Work out the probability of that event, giving your answer as a decimal.

9.On a probability scale from 0 to 1, five descriptions are used: impossible (0), unlikely (between 0 and 0.5), evens (exactly 0.5), likely (between 0.5 and 1) and certain (1). The probability that a particular bus is late is 3/8. Which description best fits this probability?

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.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.

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

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

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

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