Find expected payoffs

An insurance company offers flood insurance to customers in a certain area. Suppose they charge

$ 500

for a given plan. Based on historical data, there is a

1 %

probability that a customer with this plan suffers a flood, and in those cases, the average payout from the insurance company to the customer was

$ 10,000

Here is a table that summarizes the possible outcomes from the company's perspective:

Event	Payout	Net gain $(X)$ ‍
Flood	$$ 10,000$ ‍	$- $ 9,500$ ‍
No flood	$$ 0$ ‍	$$ 500$ ‍

Let

X

represent the company's net gain from one of these plans.

Calculate the expected net gain $E (X)$ ‍.

E (X) =

dollars

Precalculus