Question

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.

Answer 1

Suppose B₁, B₂, B₃ are three boys and G₁, G₂ are two girls.

Out of these boys and girls, a committee of two members is to be formed.

∴ S = {B₁B₂, B₁B₃, B₂B₃, B₁G₁, B₁G₂, B₂G₁, B₂G₂, B₃G₁, B₃G₂, G₁G₂}

∴ n(S) = 10

Event A: At least one girl must be a member of the committee.

A = {B₁G₁, B₁G₂, B₂G₁, B₂G₂, B₃G₁, B₃G₂, G₁G₂}

∴ n(A) = 7

P(A) = `(n(A))/(n(S))`

∴ P(A) = `7/10`

Event B: Committee must be of one boy and one girl.

B = {B₁G₁, B₁G₂, B₂G₁, B₂G₂, B₃G₁, B₃G₂}

∴ n(B) = 6

P(B) = `(n(B))/(n(S))`

P(B) = `6/10`

∴ P(B) = `3/5`