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Question
There are 3 clubs A,B,C in a town with 40,50,60 members respectively, 10 people are members of all the three clubs, 70 members belong to one club. A member is randomly selected. Find the probability that he has membership of exactly two clubs.
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Solution
Total memberships = 40 + 50 + 60 = 150
Memberships due to people in 1 club = 70
Memberships due to people in 3 clubs = 10 * 3 = 30
150 - 70 - 30 = 50 memberships due to people in 2 clubs
50/2 = 25 different people are in 2 clubs
Probability that he has membership of exactly two clubs=25/150=1/6
Total memberships = 40 + 50 + 60 = 150
Memberships due to people in 1 club = 70
Memberships due to people in 3 clubs = 10 * 3 = 30
150 - 70 - 30 = 50 memberships due to people in 2 clubs
50/2 = 25 different people are in 2 clubs
Probability that he has membership of exactly two clubs=25/150=1/6
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