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.

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Sets, Venn diagrams and tree diagrams worksheet — GCSE Foundation

Maths · GCSE Foundation · P6 · Sets, Venn diagrams and tree diagrams · 15 questions

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1.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.
(a)8
(b)36
(c)6
(d)12
2.In a survey of 45 students, 22 said they like reading, 18 said they like gaming, and 6 said they like both. Work out how many students like exactly one of reading or gaming.
(a)6
(b)40
(c)28
(d)34
3.A survey of 60 readers records: 21 read only fiction, 17 read only non-fiction, 14 read both, and the rest read neither. Work out the probability that a randomly chosen reader reads exactly one of the two types, giving your answer as a fraction in its simplest form.
(a)13/15
(b)19/26
(c)7/30
(d)19/30
4.A game has two independent stages. P(win stage 1) = 0.4, and P(win stage 2) = 0.25. Work out the probability that Ffion wins at least one of the two stages.
(a)0.1
(b)0.55
(c)0.45
(d)0.65
5.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.
(a)1/2
(b)1/9
(c)2/3
(d)1/3
6.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.
(a)The elements that are in both A and B
(b)The elements that are in B but not in A
(c)The elements that are in A but not in B
(d)The elements that are in neither A nor B
7.The numbers 1 to 10 are each written on a card. Set A is the set of multiples of 3 from 1 to 10 and set B is the set of even numbers from 1 to 10. Work out how many of the numbers from 1 to 10 are in set A but not in set B.
(a)3
(b)7
(c)2
(d)4
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.
(a)0.5
(b)0.8
(c)0.15
(d)0.65
9.Leo flips a fair coin twice. He makes a list of every possible result of the two flips, writing down what the first flip lands on and then what the second flip lands on. Work out how many of the results in his list contain at least one tail.
(a)4
(b)3
(c)1
(d)2
10.A survey of 90 people records which of two apps, X and Y, they use. 55 people use app X, 42 people use app Y, and 20 people use neither app. Work out the probability that a randomly chosen person uses both apps, giving your answer as a fraction in its simplest form.
(a)7/90
(b)3/10
(c)2/9
(d)7/9
11.A = {factors of 12} and B = {factors of 18}. Work out n(A ∩ B), the number of elements in both sets.
(a)3
(b)8
(c)6
(d)4
12.The universal set is {1, 2, 3, ..., 15}. A = {multiples of 3}. Work out n(A′), the number of elements not in A.
(a)5
(b)10
(c)12
(d)11
13.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.
(a)15
(b)10
(c)9
(d)1
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.
(a)32
(b)43
(c)11
(d)21
15.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.
(a)17
(b)8
(c)26
(d)39

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