Question

the prices of three t-shirts styles are $24, $30 and $36. the probability of choosing a $24 t-shirt is 1/6. the probability of choosing a $30 t-shirt is 1/2. the probability of choosing a $36 t-shirt is 1/3.
what is the expected value of a t-shirt?
$29
$30
$31
$32

Answer 1

$\text{Answer} : \text{The expected value of a t-shirt is \ 31.}$

Explanation:

Since we have given that

The prices of three t-shirts styles  i.e $24, $30, $36 with their probability is given by

$\frac{1}{6}, \frac{1}{2},\frac{1}{3}$

As we know that,

$E(X)= \sum_{1}^{3}x_iP(x_i)$

$\text{where} x_i \text{ is the prices of t- shirts styles}$

Now,

$x_1= \ 24 , x_2=\ 30 , x_3= 36$

and

$P(x_1)=\frac{1}{6},P(x_2)=\frac{1}{2}, P(x_3)=\frac{1}{3}$

So,

$E(X)= 24\times \frac{1}{6}+30\times\frac{1}{2}+36\times \frac{1}{3}\\=4+15+12\\=31$

So, the expected value of a t-shirt = $31.