A committee of 4 students is selected at random from a group consisting 8 boys and 4 girls. Given that there is at least one girl on the committee, calculate the probability that there are exactly 2 girls on the committee.

168/425

Event A : Atleast one girl is chosen

Event B : Exactly two girls will be chosen

P(A) = 1 - P(No girl is chosen) = 1 - P(All boys are chosen) = 1 - ⁸C₄/¹²C₄ = 1 - 14/99 

       = 85/99

P(A\(\)B) = P(Two girls are chosen) = ⁸C₂ x ⁴C₂/¹²C₄ 

    = 56/165 

P(B|A) = P(A\(\)B) / P(A) = \(\frac{ 56/165 }{85/99}\)

           = 168/425