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Question

The probability that a man aged x years will die in a year is p. The probability that out of n men A1,A2,A3,...,An each aged x,A1 will die and be first to die, is

A
1n2
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B
1(1p)n
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C
1n2(1(1p)n)
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D
1n(1(1p)n)
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Solution

The correct option is D 1n(1(1p)n)
The probability that a man does not die in a year 1p
Probability that none of the n men dies in a year (1p)n
The probability that at least one man dies in a year 1(1p)n
Since every man can die first, the chance that A1, will die first in 1n.
Hence the probability that A1, will die within a year and he will be first to die 1n(1(1p)n)

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