Question

A purse contains n coins of unknown value, a coin drawn at random is found to be a rupee, what is the chance that it is the only rupee in the purse? Assume all numbers of rupee coins in the purse to be equally likely.

Answer 1

$P=\frac{\frac{1}{n}+\frac{2}{n}+\frac{3}{n}+\frac{4}{n}+.....+\frac{n}{n}}{{}^n{C}_1}$
$=\frac{1}{n}\left(\frac{1+2+3+4+....+n}{{}^n{C}_1}\right)$
$=\frac{1}{n}\times \frac{n\left(n+1\right)}{2}\times \frac{1}{n}$
$=\frac{n+1}{2}\times \frac{1}{n}=\frac{n+1}{2n}$