A cricket club has 15 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected?

assupecoitteem81

assupecoitteem81

Answered question

2022-11-11

A cricket club has 15 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected?

Answer & Explanation

Lillianna Salazar

Lillianna Salazar

Beginner2022-11-12Added 22 answers

Let A k be the event that exactly k bowlers are selected out of the group of 5 bowlers for k = 0 , 1 , , 5. They are mutually exclusive events. Note that mutually exclusive does not mean that a team in A 4 and another team in A 5 have no member in common! It means that such teams are distinct: there is at least a member in one team that is not in the other one.
Then the required probability is
P ( A 3 A 4 A 5 ) = P ( A 3 ) + P ( A 4 ) + P ( A 5 ) .
What is P ( A k )? We choose 11 members out of 15, where k are selected among the 5 bowlers and 11 k among the remaining 15 5 members.

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