Question

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

• A. $=\left(\frac{1}{n}\right)[1-p^n]$.
• B. $=\left(\frac{1}{n}\right)[1-(1-p{)}^n]$.
• C. $=\left(\frac{1}{n}\right)\left[\right(1-p{)}^n]$.
• D. $=\left(\frac{1}{n}\right)[1-(2-p{)}^n]$.

Answer 1

The correct option is B

$=\left(\frac{1}{n}\right)[1-(1-p{)}^n]$.

Since the probability that a man aged x years will die in a year is p, therefore the probability of that man not to die in a year $=1-p.$
Hence the probability that none out of n men aged x year will die in a year $=(1-p{)}^n.$
If follows that the probability that our of n men at least one dies in a year $=1-(1-p{)}^n.$
Also, the probability that out of n men the man to die first is $A_1=\frac{1}{n}.$
$\therefore$ The required probability
$=\left(\frac{1}{n}\right)[1-(1-p{)}^n]$.