Question

A box contains $12$ mangoes out of which $5$ are rotten and rest are good. Two mangoes are randomly taken out together. If it is known that atleast one of them is good, then the probability that both are good is $\frac{p}{q}$, where $p,q$ are coprime numbers. Then the value of $|p-q|$ is

Answer 1

Required probability $=\frac{{}^7{C}_2}{{}^7{C}_2+{}^7{C}_1\cdot {}^5{C}_1}=\frac{3}{8}$
$\Rightarrow \frac{3}{8}=\frac{p}{q}$
$\Rightarrow |p-q|=5$