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.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?

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.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.

5.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.

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

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

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

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

11.A survey found that, of 250 shoppers questioned, 68% said they had used a self-checkout in the past month. A different store expects 1400 shoppers this week. Using this relative frequency, work out how many of the 1400 shoppers would be expected to have used a self-checkout in the past month.

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

13.Two goalkeepers face penalty kicks. Elin saves 34% of the penalties she faces. Noah saves 11/32 of the penalties he faces. Which statement correctly compares them?

14.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.

15.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.