Q.3 (B)(iii) A committee of two members is to be formed from three boys and two girls. Find the probability of the following events :Event A : At least one girl must be a member of the committee.Event B : Committee must be of one boy and one girl.

Doubtly Asked 24 Oct 2026 ssc 10th Save WhatsApp Report

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Answer: P(A) = 7/10, P(B) = 3/5

Let the boys be B₁, B₂, B₃ and the girls G₁, G₂.

S = {B₁B₂, B₁B₃, B₂B₃, B₁G₁, B₁G₂, B₂G₁, B₂G₂, B₃G₁, B₃G₂, G₁G₂}, n(S) = 10.

A = all committees except the three all-boy ones, n(A) = 7, so \(P(A) = \dfrac{7}{10}\).

B = {B₁G₁, B₁G₂, B₂G₁, B₂G₂, B₃G₁, B₃G₂}, n(B) = 6, so \(P(B) = \dfrac{6}{10} = \dfrac{3}{5}\).

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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