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−(1−p)n
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C
1n2(1−(1−p)n)
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D
1n(1−(1−p)n)
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Solution
The correct option is D1n(1−(1−p)n) The probability that a man does not die in a year 1−p ∴ Probability that none of the n men dies in a year (1−p)n ∴ The probability that at least one man dies in a year 1−(1−p)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−(1−p)n)