Question

a person will randomly win 1 of 5 prizes. the cash values of the 5 prizes are $5, $10, $10, $10, $20, respectively. which properly calculates the expected value of the persons winning prize?
a (5 + 10 + 20)/3 = $11.7
b most common value is $10, so $10
c 5x(1/5) + 10x(1/5) + 20x(1/5) = $7
d 5x(1/5) + 10x(3/5) + 20x(1/5) = $11

Explanation:

Step1: Recall expected - value formula

The formula for the expected value $E(X)$ of a discrete - random variable is $E(X)=\sum_{i = 1}^{n}x_ip_i$, where $x_i$ are the possible values and $p_i$ are their corresponding probabilities. Here, there are 5 prizes, so the probability of winning each prize $p=\frac{1}{5}$.

Step2: Calculate the expected value

The values of the prizes are $x_1 = 5$, $x_2 = 10$, $x_3 = 10$, $x_4 = 10$, $x_5 = 20$.
$E(X)=5\times\frac{1}{5}+10\times\frac{3}{5}+20\times\frac{1}{5}$
$=1 + 6+4$
$=11$

Answer:

D. $5\times(1/5)+10\times(3/5)+20\times(1/5)=11$