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

The expected number of men in the delegation is 0.86.

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)=(^3C_0* ^4C_2)/(^7C_2)=(2)/(7)`

`P(X=1)=(^3C_1* ^4C_1)/(^7C_2)=(4)/(7)`

`P(X=2)=(^3C_2* ^4C_0)/(^7C_2)=(1)/(7)`

The expected number of men in the delegation is

`E(x)=0* P(X=0)+1* P(X=1)+2* P(X=2)`

`E(x)=0* (2)/(7)+1* (4)/(7)+2* (1)/(7)`

`E(x)=(6)/(7)`

`E(x)\approx 0.86`

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