A survey was conducted among 50 students at a secondary school in Kingston, Jamaica, to determine their participation in Cricket (C) and Football (F). The results showed that 28 students played Cricket, 25 played Football, and 8 played neither sport. How many students played BOTH Cricket and Football?

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Question

A survey was conducted among 50 students at a secondary school in Kingston, Jamaica, to determine their participation in Cricket (C) and Football (F). The results showed that 28 students played Cricket, 25 played Football, and 8 played neither sport. How many students played BOTH Cricket and Football?

Accepted Answer

11 — Using the formula n(U) = n(C) + n(F) - n(C ∩ F) + n(neither): 50 = 28 + 25 - n(C ∩ F) + 8. Therefore 50 = 61 - n(C ∩ F), giving n(C ∩ F) = 11. Award 1 mark for correct application of the inclusion-exclusion principle. A (5) is incorrect — this results from arithmetic error. C (15) confuses the intersection with another region. D (45) incorrectly adds all values.

Answer

11

Answer

5

Answer

45

Answer

15

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