avicenna, an insurance company, offers five - year commercial property insurance policies to small…

avicenna, an insurance company, offers five - year commercial property insurance policies to small businesses. if the holder of one of these policies experiences property damage in the next five years, the company must pay out $27,400 to the policy holder. executives at avicenna are considering offering these policies for $765 each. suppose that for each holder of a policy there is a 3% chance they will experience property damage in the next five years and a 97% chance they will not.\n\nif the executives at avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? how much?\nto answer, take into account the price of the policy and the expected value of the amount paid out to the holder.\n\navicenna can expect to make money from offering these policies.\nin the long run, they should expect to make dollars on each policy sold.\n\navicenna can expect to lose money from offering these policies.\nin the long run, they should expect to lose dollars on each policy sold.\n\navicenna should expect to neither make nor lose money from offering these policies.

avicenna, an insurance company, offers five - year commercial property insurance policies to small businesses. if the holder of one of these policies experiences property damage in the next five years, the company must pay out $27,400 to the policy holder. executives at avicenna are considering offering these policies for $765 each. suppose that for each holder of a policy there is a 3% chance they will experience property damage in the next five years and a 97% chance they will not.\n\nif the executives at avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? how much?\nto answer, take into account the price of the policy and the expected value of the amount paid out to the holder.\n\navicenna can expect to make money from offering these policies.\nin the long run, they should expect to make dollars on each policy sold.\n\navicenna can expect to lose money from offering these policies.\nin the long run, they should expect to lose dollars on each policy sold.\n\navicenna should expect to neither make nor lose money from offering these policies.

Answer

Explanation:

Step1: Calculate expected payout

The probability of property - damage $p = 0.03$ and the payout in case of damage is $A = 27400$. The probability of no - damage $q=0.97$ and the payout in case of no - damage is $0$. The expected value of the payout $E(X)$ is calculated using the formula $E(X)=p\times A+q\times0$. So, $E(X)=0.03\times27400 + 0.97\times0=822$.

Step2: Calculate expected profit

The price of the policy is $765$. The expected profit $P$ per policy is the price of the policy minus the expected payout. So, $P = 765-822=- 57$.

Answer:

Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose 57 dollars on each policy sold.