Question

In a class of 10 boys and 12 girls, a committee of 4 members is to be formed. What is the probability to form a committee consisting of 2 boys and 2 girls?0.30400.40600.50600.2060

Answer 1

Consider all the different possible combinations of 4 members of the committee (b,b,b,b), (b,b,b,g),...(g,g,g,g). We need to use the binomial distribution given below

`P(k)=(nbinomialk)p^k(1-p)^(n-k)`

In our case

`k=2,n=4,p=(10)/(10+12)=(10)/(22)=(5)/(11)`

Then,

`\begin{gathered} P(2)=((4!)/(2!(4-2)!))((5)/(11))^2((6)/(11))^2 \\ \Rightarrow P(2)=6\cdot(900)/(14641) \\ \Rightarrow P(2)=0. \end{gathered}`