Question

two person are sleceted at random out fo 9 girls and 11 boys without replacement. IF 605 is fofered for selecting two girls, what is the mathetmatical expectation

Answer 1

`E(x) = 114.63`

Explanation:

Given

`Boys= 11`

`Girls = 9`

Required

Expected value of selecting two girls if 605 is offered

First, we need to calculate the number of persons.

`Total = Boys + Girls`

`Total = 11+9`

`Total = 20`

The probability of selecting the first girl is:

`P(First) = (9)/(20)`

Because, it is a selection without replacement, the number of girls and number of persons have reduced by 1 respectively.

So, the probability of selecting the second girl is:

`P(Second) = (8)/(19)`

The probability (p) of both selection being girls is:

`p=(9)/(20) * (8)/(19)`

`p=(72)/(380)`

`p=(18)/(95)`

The mathematical expectation E(x), is then calculated using:

`E(x) = n * p`

In this case:

n = Offered Amount

`n = 605`

So:

`E(x) = 605 * (18)/(95)`

`E(x) = (10890)/(95)`

`E(x) = 114.631578947`

`E(x) = 114.63`

Hence, the mathematical expectation is 114.63