Answer:
Expected value: 198.35$
Step-by-step explanation:
This problem can be done in such many ways, you can do a chart with possible values for X, you can do a graph, you can do sum and substract...However for this question, let me tell you the way that I consider is the easiest to you for understand.
First, we know how the insurance costs, which is 150,000$. We know that the girl will pay 260$, and we also know the survival probability of the girl, which is 0.999589.
Now, if the girl can survive with a probability of 0.999589, means that there is a minimum possibility that the girl dies in the year. This number is:
1 - 0.999589 = 0.000411
This is the probability that girl dies in the year.
If the insurance costs 150,000 and it's sold by 260, means that the insurance would be:
150,000 - 260 = 149,740$
Now, if you take this amount and multiply with the probability that the girl dies:
149,740 * 0.000411 = 61.54 $
This would be the cost of the insurance if the girl dies, however, we need to substract too the amount of the insurace if the girl lives. this number is taken out of the probability that the girl lives with the cost of the insurance:
260 * 0.999589 = 259.89$
Finally, the expected value of this policy for the company will be:
Expected value = 259.89 - 61.54 = 198.35$
This would be the expected value that the insurance company will expect after the policy is sold.
