# A Committee of 4 Students is Selected at Random from a Group Consisting of 7 Boys and 4 Girls. Find the Probability that There Are Exactly 2 Boys in the Committee, Given that - Mathematics

Sum

A committee of 4 students is selected at random from a group consisting of 7 boys and 4 girls. Find the probability that there are exactly 2 boys in the committee, given that at least one girl must be there in the committee.

#### Solution

Let A: exactly 2 boys are in the committee,

B: at least one girl must be in the committee.

So,
P(B) = (""^4"C"_1 xx ""^7"C"_3 + ""^4"C"_2 xx ""^7"C"_2 + ""^4"C"_3 xx ""^7"C"_1 + ""^4"C"_4)/(""^11"C"_4)

= (59)/(66) &

"P" ("A" ∩ "B") = (""^4"C"_2 xx ""^7"C"_2)/(""^11"C"_4) = (21)/(55).

= Now

"P"("A"/"B") = ("P" ("A" ∩ "B"))/("P"("B")

= (21/55)/(59/66)

= (126)/(295).

Concept: Introduction of Probability
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