# An insurance agent insures lives of 5 men, all of the same age and in good health. The probability that a man of this age will survive the next 30 years is known to be 2/3 . Find the probability that in the next 30 years at most 3 men will survive. - Mathematics and Statistics

An insurance agent insures lives of 5 men, all of the same age and in good health. The probability that a man of this age will survive the next 30 years is known to be 2/3 . Find the probability that in the next 30 years at most 3 men will survive.

#### Solution

p=2/3, q=1-2/3=1/3, n=5

P(x<=3)=1-P(x>3)

=1-[P(4)-+P(5)]

=1-[""^5C_4(2/3)^4(1/3)^1+""^5C_5(2/3)^5]

=1-[5xx16/81xx1/3+1xx32/343]

=1-16/243xx7

=1-112/243

=(243-112)/243

=131/243

=0.539

Concept: Conditional Probability
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