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 \( x \), man \( A_1 \) will die in a year and be the first to die is:
The probability that none of them will die is: \[ (1 - p)^n \] Hence, the probability that at least one of them will die is: \[ 1 - (1 - p)^n \] Now, if we consider the order, the probability that \( A_1 \) is the first to die among \( n \) people is: \[ \frac{1}{n} \left( 1 - (1 - p)^n \right) \]
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