Question

An insurance salesman sells policies to 5 men, all of identical age. According to the actuarial tables, the probability that a man of this particular age will be alive 30 years hence is 2/3. Find the probability that in 30 years
a. All 5 men
b. At least 3 men
c. Only 2 men
d. At least 1 man will be alive.

Answer 1

Step-by-step explanation:

n = 5

p = 2/3

q = 1/3

P(x) = C(n,r) * p^x * q^(n-x)

a) P(x=5) = C(5,5) * (2/3)^5 = 32/243

b) P(x>=3) = C(5,3) * (2/3)^3 * (1/3)^2 + C(5,4) * (2/3)^4 * (1/3)^1 + C(5,5) * (2/3)^5 = 192/243

c) P(x=2) = C(5,2) * (2/3)^2 * (1/3)^3 = 40/243

d) P(x>=1) = 1 - P(x=0) = 1 - C(5,0) * (1/3)^5 = 242/243