Answer :
Answer:
The expected number of men in the delegation is 0.86.
Step-by-step explanation:
Number of men = 3
Number of women = 4
A delegation of 2 is selected.
Let X be the number of men selected. So, the possible values of X are 0,1,2.
[tex]P(X=0)=\dfrac{^3C_0\times ^4C_2}{^7C_2}=\dfrac{2}{7}[/tex]
[tex]P(X=1)=\dfrac{^3C_1\times ^4C_1}{^7C_2}=\dfrac{4}{7}[/tex]
[tex]P(X=2)=\dfrac{^3C_2\times ^4C_0}{^7C_2}=\dfrac{1}{7}[/tex]
The expected number of men in the delegation is
[tex]E(x)=0\times P(X=0)+1\times P(X=1)+2\times P(X=2)[/tex]
[tex]E(x)=0\times \dfrac{2}{7}+1\times \dfrac{4}{7}+2\times \dfrac{1}{7}[/tex]
[tex]E(x)=\dfrac{6}{7}[/tex]
[tex]E(x)\approx 0.86[/tex]
Therefore, the expected number of men in the delegation is 0.86.