Question

A purse contains 100 coins of unknown value, a coin drawn at random is found to be a rupee, The chance that it is the only rupee in the purse, is (Assume all numbers of rupee coins in the purse to be equally likely.)

• A. $\frac{1}{5050}$
• B. $\frac{2}{5151}$
• C. $\frac{1}{4950}$
• D. $\frac{2}{4950}$

Answer 1

Answer: (A)

A: coin drawn found to be rupee

$P\left(B_1/A\right)=\frac{P\left(A\cap B_1\right)}{P(A)}=\frac{P\left(B_1\right)\cdot P\left(A/B_1\right)}{P(A)}=\frac{\frac{1}{n}}{\frac{1}{n}+\frac{2}{n}+\frac{3}{n}+\dots .+\frac{n}{n}}=\frac{1}{1+2+3+\dots ..+n}$
$=\frac{2}{n(n+1)}=\frac{2}{100\cdot 101}=\frac{1}{5050}$