Question 1160096: Question3: 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 by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! a. This is (2/3)^5=32/243 or 0.132
Look at the rest of the possibilities:
For 1 to be alive is 5(2/3)(1/3)^4=10/243
For 2 to be alive is 10(2/3)^2(1/3)^3=40/243
for 3, it is 10(2/3)^3(1/3)^2=80/243
for 4, it is 5(2/3)^4(1/3)=80/243
For 0, it is (1/3)^5=1/243
Those all add up to 243/243
b. At least 3 men means 3,4,5 or 192/243 or 0.7901
c. For 2 men, it is 40/243 or 0.1646
d. At least 1 man means 1-p(0 men) or 242/243 or 0.9959
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