If the extended warranty on a car costs $200 and average repair bill is $1000, then what is the probability of a breakdown if the company offering the warranty expects to break even?
@reneesonny Let p denote the probability of a breakdown. The *expected* repair bill is the product of such a repair bill with this probability of it being required, i.e. the probability of a breakdown. So the expected repair bill is 1000p. This is what the insurance company *expects* the cost to be on average, i.e. this is its *risk*. For the company to break even, it has to ensure that the warranty it charges the customer exactly counterbalances this risk. So we have 1000p = 200, i.e. p = 200/1000 = 0.2 (= 1/5)