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

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:

$Pr(X_1=1)=\frac{4}{14}=\frac{2}{7}$

So we end up with:

$EX=\frac{16}{7}$

We can conclude that the correct answer is:

Answer:$\frac{16}{7}$