A small town has 1,000 people, 600 of whom are healthy and 400 of whom are sick. The annual expected medical claims of the healthy and sick are $500 and $9,000, respectively. If the insurance company cannot determine who is healthy and who is sick prior to the purchase of insurance, the annual premium must be at least $. a. 3,900
b. 9,000
c. 2,000
d. 4,750

a. 3,900

Explanation:

We find the probability of healthy persons & the weak out of the total population in the town.

Probability of healthy persons

P(h) = 600/1000

P(h) = 0.6

Probability of weak persons

P(w) = 400/1000

P(w) = 0.4

We find the pay off for both the healthy and the weak, then add up to get the expected value or the minimal annual premium

Expected Value = 0.6*$500 + 0.4*$9000

Expected Value = $300 + $9000

Expected Value = $3,900

So, the annual premium must be at least $3,900.

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