SOLUTION: There is roughly an 80% chance that a person of age 20 will be alive at 65 suppose that 3 age 20's are selected at random. Find the probability that the number alive at 65 will be

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Question 1203779: There is roughly an 80% chance that a person of age 20 will be alive at 65 suppose that 3 age 20's are selected at random. Find the probability that the number alive at 65 will be exactly two(2)
b) Atleast one
c) Atmost two
d) Less than one
e) Write the probability distribution
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The logical way to answer these questions is to do part (e) first and -- to verify that your calculations are correct -- verify that the sum of the probabilities is 1; then answer the individual questions.

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NOTE!
If you are just learning how to calculate binomial probabilities, it is good practice -- if the number of cases is small -- to calculate the probabilities of all possible outcomes and verify that their sum is 1
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3 of 3 alive at age 65:
C%283%2C3%29%28%28.8%29%5E3%29%28%28.2%29%5E0%29=%281%29%28.512%29%281%29=.512

2 of 3 alive at age 65:
C%283%2C2%29%28%28.8%29%5E2%29%28%28.2%29%5E1%29=%283%29%28.64%29%28.2%29=.384

1 of 3 alive at age 65:
C%283%2C1%29%28%28.8%29%5E1%29%28%28.2%29%5E2%29=%283%29%28.8%29%28.04%29=.096

0 of 3 alive at age 65:
C%283%2C0%29%28%28.8%29%5E0%29%28%28.2%29%5E3%29=%281%29%281%29%28.008%29=.008

.512+.384+.096+.008 = 1.000 so the calculations should be good.

ANSWERS:
(a) exactly 2: 0.384
(b) at least 1: 1-.008 = 0.992
(c) at most 2: 1-.512 = 0.488
(d) less than 1: 0.008
(e) (see above)