Interpret the Mean of a Discrete Random Variable as an Expected

Short Answer

Interpret the Mean of a Discrete Random Variable as an Expected Value
-An automobile insurance company estimates the following loss probabilities for the next year on a $\$ 25,000$ sports car:
$\begin{array} { l r } \text { Total loss: } & 0.001 \\ 50 \% \text { loss: } & 0.01 \\ 25 \% \text { loss: } & 0.05 \\ 10 \% \text { loss: } & 0.10 \end{array}$
Assuming the company will sell only a $\$ 500$ deductible policy for this model (i.e., the owner covers the first $\$ 500$ damage), how much annual premium should the company charge in order to average $\$ 450$ profit per policy sold?