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.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.

3.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.

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

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

6.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?

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

9.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.

10.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?

11.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?

12.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?

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

14.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.

15.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.