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, A_n` each aged `x ,A_1` will die in an year and be the first to die is `1-(1-p)^n` b. `(1-p)^n` c. `1//n[1-(1-p)^n]` d. `1//n(1-p)^n`

Options

A. `1-(1-p)^(n)`
B. `(1-p)^(n)`
C. `1//n[1-(1-p)^(n)]`
D. `1//n(1-p)^(n)`

Answer

C

Explanation

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 `(1-p)^(n).` Therefore, the probability that at least one man dies in a year is `1-(1-p)^(n).` The probability that our of n men, `A_(1)` dies first in 1/n. Since this event is independent of the event that at least one man dies in a year, the probability that `A_(1)` dies in the year and he is the first one to die is `1//n[1-(1-p)n].`