Question

A newly formed life insurance company has underwritten term policies on 120 women between the ages of forty and forty-four. Suppose that each woman has a 1/150 probability of dying during the next calendar year, and that each death requires the company to pay out $50,000 in benefits. Approximate the probability that the company will have to pay at least $150,000 in benefits next year

Answer 1

The probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

The probability of dying:

P(dying) = 1/150

P(living) = 1 - P(dying) = 1 - 1/150 = 140/150

There are 120 women.

P(x≥3) = 1 - [P(x=0) +P(x=1) + P(x=2)]

$\rm P(x\geq 3)=1-[(120 \ choose \ 0)(1/150)^0)((149/150)^{120})+$  

                  $\rm (120 \ choose \ 1) ((1/150)^1) ((149/150)^{119}) +$

                  $\rm (120 \ choose \ 2)((1/150)^2)((149/150)^{118})]$

P(x≥3) = 0.047

Thus, the probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.

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