Let p denote the probability that a man aged x years will die in a year. The probability that out of n men $A_1,A_2,A_3,....A_n$ each aged x, $A_1$will die in a year and will be the first to die is

Let Ei denote the event that Ai dies in a year, then $P\left(E_i\right)=p$ and $P\left(E_i^{\text{'}}\right)=1-p$ for I = 1, 2, …..n P (none of A1, A2, …. A3 dies in a year) $=P(E_1^{\text{'}}\cap E_2^{\text{'}}\cap E_n^{\text{'}})=P\left(E_1^{\text{'}}\right)P\left(E_2^{\text{'}}\right)\mathrm{....}P\left(E_n^{\text{'}}\right)={(1-p)}^n$
Because E1, E2,……En are independent.
Let E denote the event that at least one of $A_1,A_2,\mathrm{.......}{A}_n$ dies in a year, then $P\left(E\right)=1-P(E_1^{\text{'}}\cap E_2^{\text{'}}\cap \mathrm{....}\cap E_n^{\text{'}})=1-{(1-p)}^n$
Let F denote the event that A1 is the first to die, then $P(F/E)=\frac{1}{n}.Also,$ P(F) = P(E).P(F/E) =  $\frac{1}{n}\left[1-{(1-p)}^n\right]$