Answer to Question #338399 in Statistics and Probability for Developer

Question

Thirty people, who are of the same age and the same health status, are

insured with the same insurance company. Using life tables, the company

estimates that the probability for a randomly chosen person among these 30

to be alive in 15 years from now is 0:8.

(i) What is the probability that not all 30 people will be alive in 15 years time?

(ii) What is the probability that at least one person will be alive?

Answer 1

Let $X=$ the number of person who will be alive:$X\sim Bin(n, p).$

Given $n=30, p=0.8, q=1-p=0.2.$

(i)

$$P(X<30)=1-P(X=30)$$

$$=1-\dbinom{30}{0}(0.8)^{30}(0.1)^{30-30}$$

$$=0.99876205996$$

(ii)

$$P(X\ge1)=1-P(X=0)$$

$$=1-\dbinom{30}{0}(0.8)^{0}(0.2)^{30-0}$$

$$> 0.999999$$