Answer:
The insurance company will gain an expected value $176.66032
Step-by-step 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