Suppose a life insurance company sells a $290 comma 000 one-year term life insurance policy to a 20-year-old female for $280. the probability that the female survives the year is 0.999644. compute and interpret the expected value of this policy to the insurance company.

The insurance company will gain an expected value $176.66032

Explanation:

The expected value is the gain or loss of an event and is calculated each outcome by its probability.

In our case we have to consider all events as follows;

The probability of dying means the insurance company will have a loss of $290,000 and gain $280 which is the cost of the policy. The probability of this happening=(1-probability of living)=(1-0.999644)=0.000356

The probability of living means the insurance company will gain $280, and the probability of this happening=0.999644

The gain or loss from death=280-290,000=-$289,720

The gain or loss from living=$280

Expected value=(The loss from death×probability of death)+(The gain from living×probability of living)

where;

The loss from death=-$290,000

Probability of death=0.000356

The gain from living=$280

Probability of living=0.999644

replacing;

Expected value=(-290,000×0.000356)+(280×0.999644)

Expected value=(-103.24+279.90032)

Expected value=$176.66032

The insurance company will gain an expected value $176.66032

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