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

Answer:

$E(x) = 114.63$

Step-by-step 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:

$P(First) = \frac{9}{20}$

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:

$P(Second) = \frac{8}{19}$

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

$p=\frac{9}{20} * \frac{8}{19}$

$p=\frac{72}{380}$

$p=\frac{18}{95}$

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

$E(x) = n * p$

In this case:

n = Offered Amount

$n = 605$

So:

$E(x) = 605 * \frac{18}{95}$

$E(x) = \frac{10890}{95}$

$E(x) = 114.631578947$

$E(x) = 114.63$

Hence, the mathematical expectation is 114.63