Question

An insurance company estimates the probability of an earthquake in the next year to be 0.0013.
The average damage done by an earthquake it estimates to be $60,000. If the company offers
earthquake insurance for $100, what is their expected value of the policy?

Answer 1

E[P] = $100/0.0013 = $76923.08

Answer 2

The expected value of the policy is simply the mean or average of the policy.

The expected value of the insurance policy is -$22

Given

$P(x) = 0.0013$ --- the probability of an earthquake

$x = \ 100$ --- the offer

The expected value of the policy is:

$E(x) =\sum x \times P(x)$

So, we have:

$E(x) = \ 60,000 \times 0.0013 +(-\ 100) \times 100\%$

The 100% means they pay the whole $100 when an earthquake occurs

So, we have:

$E(x) = -\ 22$

Hence, the expected value of the insurance policy is -$22

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