In a group of 60 students, 30 play cricket, 25 play tennis and 20 play badminton. Also 12 play cricket and tennis, 8 play tennis and badminton, 10 play cricket and badminton, and 5 play all three games. One student is picked at random. What is the probability that the student plays none of the three games?

Question

Accepted Answer

1/6. By inclusion–exclusion the number playing at least one game is 30 + 25 + 20 − 12 − 8 − 10 + 5 = 50. So 60 − 50 = 10 students play none of them, and the probability is 10/60 = 1/6. The value 5/6 is the probability of playing at least one game — the forgotten complement.

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