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Chapter: Probability· Mathematics Part 1 (Algebra)

Asked in: March 2025 board paperQ.11 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…

Asked in: March 2025 board paper

Q.11 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.

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Answer: \(P(A) = \dfrac{7}{10}\), \(P(B) = \dfrac{3}{5}\)

Let the boys be \(B_1, B_2, B_3\) and the girls \(G_1, G_2\). A committee is a pair, so order does not matter.

S = {\(B_1B_2, B_1B_3, B_2B_3, B_1G_1, B_1G_2, B_2G_1, B_2G_2, B_3G_1, B_3G_2, G_1G_2\)}, n(S) = 10

Event A: at least one girl. All pairs except the three all-boy pairs: n(A) = 10 − 3 = 7, \(P(A) = \dfrac{7}{10}\).

Event B: one boy and one girl. B = {\(B_1G_1, B_1G_2, B_2G_1, B_2G_2, B_3G_1, B_3G_2\)}, n(B) = 6, \(P(B) = \dfrac{6}{10} = \dfrac{3}{5}\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report
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