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 $23,900 to the policy holder. Executives at Avicenna are considering offering these policies for $956 each. Suppose that for each holder of a policy there is a 4% chance they will experience property damage in the next five years and a 96% chance they will not.(If necessary, consult a list of formulas.)If 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?To answer, take into account the price of the policy and the expected value of the amount paid out to the holder.Avicenna can expect to make money from offering these policies.In the long run, they should expect to makedollars on each policy sold.Avicenna can expect to lose money from offering these policies.In the long run, they should expect to losedollars on each policy sold.Avicenna should expect to neither make nor lose money from offering these policies.
Question
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 956 each. Suppose that for each holder of a policy there is a 4% chance they will experience property damage in the next five years and a 96% chance they will not.(If necessary, consult a list of formulas.)If 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?To answer, take into account the price of the policy and the expected value of the amount paid out to the holder.Avicenna can expect to make money from offering these policies.In the long run, they should expect to makedollars on each policy sold.Avicenna can expect to lose money from offering these policies.In the long run, they should expect to losedollars on each policy sold.Avicenna should expect to neither make nor lose money from offering these policies.
Solution
To answer this question, we need to calculate the expected value of the payout for each policy.
The expected value is calculated as follows:
Expected Value = (Probability of an event) x (Payout for the event)
In this case, the probability of the event (property damage) is 4% or 0.04, and the payout for the event is $23,900.
So, the expected value of the payout for each policy is:
Expected Payout = 0.04 x 956
This means that for each policy sold, Avicenna can expect to pay out $956 on average.
Now, if the company is considering offering these policies for $956 each, this means that the price of the policy is exactly equal to the expected payout.
Therefore, Avicenna should expect to neither make nor lose money from offering these policies. The income from selling the policies would, on average, exactly cover the payouts.
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