The student mess committee of a reputed Engineering College has n members. Let P be the event that the Committee has students of both sexes and let Q be the event that there is at most one female student in the committee. Assuming that each committee member has probability 0.5 of being female, the value of n for which the events A and B are independent is
Explanation:
P = event that both males and females are present in the committee = 1/n + 2/n +....+ (n – 1)/n = [1 + 2 + 3 + … + (n – 1)]/n
= [(n)(n − 1)/2n] = (n – 1)/2
Q = probability that at most one female is present in the committee = 1/n Probability of P⋂Q = P × Q P ⋂ Q = 1/n as “only one female in the committee is the intersection of the two events”.
∴ (1/n) = [(n − 1)/2] × (1/n)
∴ n – 1 = 2 i.e. n = 3
Hence, option (b).
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