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Question

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


A

=(1n)[1pn].

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B

=(1n)[1(1p)n].

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C

=(1n)[(1p)n].

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D

=(1n)[1(2p)n].

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Solution

The correct option is B

=(1n)[1(1p)n].


Since the probability that a man aged x years will die in a year is p, therefore the probability of that man not to die in a year =1p.
Hence the probability that none out of n men aged x year will die in a year =(1p)n.
If follows that the probability that our of n men at least one dies in a year =1(1p)n.
Also, the probability that out of n men the man to die first is A1=1n.
The required probability
=(1n)[1(1p)n].


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