Question

From a group of 3 men and 4 women, a delegation of 2 is selected. What is the expected number of men in the delegation?

Answer 1

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.

$P(X=0)=\dfrac{^3C_0\times ^4C_2}{^7C_2}=\dfrac{2}{7}$

$P(X=1)=\dfrac{^3C_1\times ^4C_1}{^7C_2}=\dfrac{4}{7}$

$P(X=2)=\dfrac{^3C_2\times ^4C_0}{^7C_2}=\dfrac{1}{7}$

The expected number of men in the delegation is

$E(x)=0\times P(X=0)+1\times P(X=1)+2\times P(X=2)$

$E(x)=0\times \dfrac{2}{7}+1\times \dfrac{4}{7}+2\times \dfrac{1}{7}$

$E(x)=\dfrac{6}{7}$

$E(x)\approx 0.86$

Therefore, the expected number of men in the delegation is 0.86.