Another probability problem that really need your Help!?

Question

Suppose a life insurance company insures the lives of 5000 men aged 42. If actuarial studies show the probability that any 42-year-old man will die in a given year to be 0.01, find the exact probability that the company will have to pay x=4 claims during a given year.

Answer 1

The random variable being described here has a binomial distribution B(n, p) with n=5000 (the number of 42-year-olds insured) and p=0.01 (the probability an individual dies in a given year). The probability the number of deaths is equal to 'k' is then

nCk * p^k * (1 - p)^(n - k).

Calculating this for n=5000, k=4 and p=0.01 yields

4.06 * 10^(-17)

to significant figures.