Question

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

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

Answer 1

Answer: (A)

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

The probability that a man aged $x$ year dies in a year $=p$
The probability that a man aged $x$ year does not die in a year $=1-p$
The probability that out of $n$ men none dies in that year $=(1-p)(1-p)(1-p)...n$ times $={(1-p)}^n$
The probability that a least one man dies in that year$=1-p$ (none dies in that year ).
$=[1-{(1-p)}^n]$
Also the probability that out of $n$ men, $A_1$ will die is $\frac{1}{n}$.
Thus the required probability $=\frac{1}{n}[1-{(1-p)}^n]$