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Question
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`
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