Printable · GCSE Foundation · ages 14-16
Sets, Venn diagrams and tree diagrams worksheet — GCSE Foundation
Fifteen questions on "sets, venn diagrams and tree diagrams" — DfE statement P6. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Sets, Venn diagrams and tree diagrams worksheet — GCSE Foundation
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- 1.The universal set is {1, 2, 3, ..., 30}. Set A is the set of multiples of 4 between 1 and 30. Work out n(A′), the number of elements not in A.
- 2.At a gym, 70 members are asked whether they use the pool or the sauna. 38 use the pool, 30 use the sauna, and 12 use neither. Work out n(P ∩ S), the number of members who use both the pool and the sauna.
- 3.At a youth club, 65 members are asked which sports they play. 27 play football, 21 play basketball, and 9 play both. Work out the number of members who play neither sport.
- 4.At a gym, 45 members are surveyed. 24 use the running machines, 20 use the weights machines, and 9 use both. Work out how many of the 45 members use neither machine.
- 5.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.
- 6.A Venn diagram shows two sets, P and Q, inside a universal set. n(P) = 34, n(Q) = 27, n(P ∩ Q) = 11, and n(ξ) = 90, where ξ is the universal set. Work out n((P ∪ Q)′), the number of elements in neither P nor Q.
- 7.A fair coin is flipped and an ordinary fair dice is rolled. Every possible result is listed in a table. Work out how many different results the table contains altogether.
- 8.Priya spins a fair spinner with P(red) = 0.3, and separately flips a fair coin with P(heads) = 0.5. Using a tree diagram, work out the probability that she gets red AND heads.
- 9.Two fair spinners are each numbered 1, 2 and 3. Priya spins both spinners together and records the two numbers as a pair, listing every possible outcome systematically in a grid. Work out the probability that the two numbers are the same.
- 10.A bag contains one red counter and one blue counter. Josh takes a counter, notes its colour, puts it back, then takes a counter again. He draws a tree diagram to show every possible pair of colours. Work out how many outcomes are on his tree diagram.
- 11.A bag contains 4 red counters and 6 blue counters. A counter is taken at random, its colour noted, and it is put back in the bag before a second counter is taken at random. Work out the probability that the two counters are different colours. Give your answer as a fraction in its simplest form.
- 12.In a class of 32 pupils, 19 study geography and 15 study history. 8 study both subjects. Work out n(G ∪ H), the number of pupils who study geography or history or both.
- 13.A bag contains 5 red counters and 3 blue counters. A counter is taken at random, its colour is noted, and it is put back in the bag before a second counter is taken at random. Work out the probability that both counters are the same colour.
- 14.At a leisure centre, 50 members are asked which activities they do. 32 do yoga, 24 do pilates, and 11 do both. Work out how many members do yoga only, and not pilates.
- 15.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.
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