Probability worksheet — GCSE Foundation

1.A bag contains 2 white counters and 8 black counters. One counter is taken at random from the bag. Work out the probability that the counter is not black.

2.A bag contains counters that are red, blue or green only. The probability that a counter taken at random is not red is 0.8. The bag contains 25 counters in total. Work out how many of the counters are red.

3.An ordinary fair dice is rolled once. Set A is the set of even scores and set B is the set of scores greater than 4. Work out the probability that the score rolled is in set A or in set B or in both.

4.At a tombola stall, each ticket wins a toy, wins a sweet or wins nothing, and no ticket can win more than one of these. The probability that a ticket wins a toy is 0.15 and the probability that it wins a sweet is 0.4. Work out the probability that a ticket wins neither a toy nor a sweet.

5.A jar contains counters that are pink, gold or grey only. The probability that a counter taken at random is pink is 0.2 and the probability that it is gold is 0.45. The jar contains 60 counters in total. Work out the number of grey counters.

6.The probability that a machine completes a task successfully is 0.85. Work out the probability that the machine does not complete the task successfully.

7.Oliver flips three fair coins at the same time. Work out the probability that exactly two of the three coins land on heads.

8.A fair coin is flipped three times. Work out the probability of getting at least one head.

9.A grower knows that the probability that one of their seeds germinates is 0.6. The grower wants to expect 300 of the seeds to germinate. Work out how many seeds the grower should plant.

10.Two sets, A and B, sit inside a universal set. A region of a Venn diagram is described by the notation A ∩ B′. Work out which of these describes that region.

11.Five balls numbered 1, 2, 3, 4 and 5 are in a bag. Two of them are taken out together at random. Work out the probability that the two numbers on them add up to more than 7.

12.A biased spinner is spun 200 times. It lands on red 70 times, on blue 50 times, and on green 80 times. Using these results, work out the expected number of times the spinner does NOT land on red, in 500 spins of the same spinner.

13.The probability that Priya's dentist appointment overruns is 0.35. Work out the probability that it does not overrun.

14.A fair coin is flipped and a fair three-sided spinner, labelled X, Y and Z, is spun. Every outcome is listed as a pair, such as (H, X). Work out the probability that the outcome is a head and Z.

15.The probability that Priya scores with a netball shot is 3/4. She takes two shots, and the shots are independent. Work out the probability that she scores with her first shot but misses her second shot.