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

Question

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

Infinity Learn · Accepted Answer

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)". Therefore, the probability that at least one man diesin a year is $$1$$ $$-$$ (1$$ $$-$$ $$p)". The probability that out of n men, $$A1$$ dies first $$is1n$$. Since this event is independent of the eventthat 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 $$1/n1$$−$$(1$$−$$p)n$$

$If p is the probability that a man aged x will die in a year, then the probability that out of n men A_{1}, A_{2}, \dots, A_{n} each$
$aged x, A_{1} will die in an year and be the first to die is$

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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,…,An each aged x,A1 will die in an year and be the first to die is

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$If p is the probability that a man aged x will die in a year, then the probability that out of n men A_{1}, A_{2}, \dots, A_{n} each$
$aged x, A_{1} will die in an year and be the first to die is$