Answer to Question #112057 in Statistics and Probability for Jack pak

Question

(a) An insurance salesman sells policies to 5 men, all of identical age in good health.
According to the actuarial tables the probability that a man of this particular age will be
alive 30years hence is 2
3
. Find the probability that in 30 years
(i) All men will be alive
(ii) At least 3men will be alive
(iii) Only two men will be alive
(iv) At least 1 man will be alive

Answer 1

1) Probability that all men will be alive: P=(2/3)^5 = 32/243.

2) Probability that at least 3 men will be alive: 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 = 80/243+80/243+32/243=192/243.

3) Only two men will be alive : P(x=2)=C(5,2) * (2/3)^2 * (1/3)^3 = 40/243.

4) At least 1 man will be alive: P(x>=1) = 1 - P(x=0) = 1 - C(5,0) * (1/3)^5 = 242/243.