Question

Suppose you are interested in insuring a car stereo for $600 against theft. An insurance company charges a premium of $80 for coverage for 1 year, claiming an empirically determined probability of 0.8 that the stereo system will be stolen some time during the year.

(a) What is the insurance company's expected profit?

(b) What is your expected return from the insurance company if you take out this insurance?

Answer 1

a) For Insurance company, the probability table will be:

Profit	Probability
$600	P(Not stolen) = 1 - 0.8 = 0.2
$(80 - 600) = - $520	0.8

Hence,

Expected profit

= $600*0.2 - $520*0.8

= - $296

This indicates that the insurance company will be having a loss of $296 per insurance policy.

b) My expected return = Loss of Insurance company = $296