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

Let the probability that a man aged x dies in a year p. Thus, the probability that a man aged x does not die in a year is 1 - p. The probability that all n men aged x do not die in a year is (1 - p)n. Therefore, the probability that at least one man dies in a year is 1 - (1 - p)n. The probability that out of n men, A1 dies first is 1/n. Since this event is independent of the event that at least one man dies in a year, the probability that A1 dies in the year and he is the first one to die is 1/n [1 - (1 - p)n].

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

Let the probability that a man aged x dies in a year p. Thus, the probability that a man aged x does not die in a year is 1 - p. The probability that all n men aged x do not die in a year is (1 - p)n. Therefore, the probability that at least one man dies in a year is 1 - (1 - p)n. The probability that out of n men, A1 dies first is 1/n. Since this event is independent of the event that at least one man dies in a year, the probability that A1 dies in the year and he is the first one to die is 1/n [1 - (1 - p)n].

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

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$1 - (1 - p)^{n}$

$(1 - p)^{n}$

$1 / n [1 - (1 - p)^{n}]$

$1 / n (1 - p)^{n}$

answer is C.

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Detailed Solution

Let the probability that a man aged x dies in a year p. Thus, the probability that a man aged x does not die in a year is 1 - p. The probability that all n men aged x do not die in a year is (1 - p)ⁿ. Therefore, the probability that at least one man dies in a year is 1 - (1 - p)ⁿ. The probability that out of n men, A₁ dies first is 1/n. Since this event is independent of the event that at least one man dies in a year, the probability that A₁ dies in the year and he is the first one to die is 1/n [1 - (1 - p)ⁿ].

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