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  4. 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.)

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Q. 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.)

Probability - Part 2

Solution:

A: coin drawn found to be rupee
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$P\left(B_1 / A\right)=\frac{P\left(A \cap B_1\right)}{P(A)}=\frac{P\left(B_1\right) \cdot P\left(A / B_1\right)}{P(A)}=\frac{\frac{1}{n}}{\frac{1}{n}+\frac{2}{n}+\frac{3}{n}+\ldots .+\frac{n}{n}}=\frac{1}{1+2+3+\ldots . .+n}$
$=\frac{2}{ n ( n +1)}=\frac{2}{100 \cdot 101}=\frac{1}{5050}$