An insurance company sells car insurance, with an obligation to pay 100, 000$ in

Question

An insurance company sells car insurance, with an obligation to pay 100, 000$ in case
of an accident. There are four caterogies of people:
• teenagers: N1 = 1500, p = 0.05%;
• young adults with college education: N2 = 2000, p = 0.01%;
• young adults without college education: N3 = 1500, p = 0.03%;
• middle-aged people: N4 = 3000, p = 0.02%.
The first number refers to the quantity of people in each category. The second number refers to the
probability of an accident for a given person in this category. The company wants to pay all the claims
using money collected from premiums. It wants to be able to do this with probability 90% or more. What
is the amount of money it should collect?

Explanation / Answer

We find out the expected value of money it might be required to pay.

Thus,

Thus, 2 people out of 8000 would ask for claims on an average.

So,

amount asked from each person should be : 2 * 100000 / 8000

= 25 $ as premium from each person to break even.

People Probabilty Mean 1500 0.05 0.75 2000 0.01 0.2 1500 0.03 0.45 3000 0.02 0.6 Total 8000 2

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