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Question

If p is the probability that a managed x will die in a year, find the probability that out of n men A1,A2,.....An each aged x. A1 will die in a year and be the first to die is

A
(1/n)[1(1p)n].
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B
[1(1p)n].
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C
(1/n)[(1p)n].
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D
[(1p)n].
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Solution

The correct option is B (1/n)[1(1p)n].
The probability that a man aged x year dies in a year =p
The probability that a man aged x year does not die in a year =1p
The probability that out of n men none dies in that year =(1p)(1p)(1p)...n times =(1p)n
The probability that a least one man dies in that year=1p (none dies in that year ).
=[1(1p)n]
Also the probability that out of n men, A1 will die is 1n.
Thus the required probability =1n[1(1p)n]

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