Relative frequency and the probability scale worksheet — GCSE Foundation

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

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

3.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.

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.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.

6.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?

7.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?

8.The probability that Amelia's bus is late on a school morning is 9/10. Write this probability as a percentage.

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

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

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

12.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?

13.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.

14.An ordinary six-sided dice, numbered 1 to 6, is rolled 30 times and lands on a 6 seven times. Ravi says the theoretical probability of rolling a 6 and the relative frequency of rolling a 6 in this trial are the same number. Is Ravi right?

15.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.