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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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