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.}`

Step-by-step explanation:

Since we have given that

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

`(1)/(6), (1)/(2),(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)=(1)/(6),P(x_2)=(1)/(2), P(x_3)=(1)/(3)`

So,

`E(X)= 24* (1)/(6)+30*(1)/(2)+36* (1)/(3)\\=4+15+12\\=31`

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