Question

An agent sells life insurance policies to five equally aged, healthy people. According to
recent data, the probability of a person living in these conditions for 30 years or more is
2/3. Calculate the probability that after 30 years:  

a) All five people are still living.

b) At least three people are still living.
c) Exactly two people are still living.

Answer 1

Probability of a person living in these conditions for 30 years or more = p= 2/3

Total number of samples =n = 5

Let X be the number of people living.

X ~ Binomial(n=5, p=2/3)

Probability mass function of X :

a) Probability that all five people are still living :

   

b) Probability that at least three people are still living :   

c) Probability that exactly two people are still living :