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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.

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#### 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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