Question

A committee of four students will be selected from a list that contains six Grade 9 students and eight Grade 10 students. What is the expected number of Grade 10 students on the committee?

Answer 1

Step-by-step explanation:

Give the Grade 10 students the numbers 1,2,...,8, and for

`i\in\lbrace1,...,8\rbrace`

Let

`X_i\text{ = 1}`

if the Grade 10 student with the number i is chosen.

On the other hand, let

`X_i\text{ = 0}`

otherwise. Then:

`X\text{ : = X}_{1\text{ }}+\text{ .... + X}_8`

is the number of Grade 10 students that are chosen.

With linearity of expectation and symmetry we find:

`EX=8EX_1\text{ = 8Pr\lparen X}_1=1\text{\rparen}`

In total there are 14 students and 4 of them will be chosen, so:

`Pr(X_1=1)=(4)/(14)=(2)/(7)`

So we end up with:

`EX=(16)/(7)`

We can conclude that the correct answer is:

Answer:
`(16)/(7)`