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.
Answer & explanation
Correct answer: option 4
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