Question

A box contain 10 mangoes out of which four are rotten. Two mangoes are taken out together. If one of them is found good and p is probability the other is also good, then value of 13p is ___.

Answer 1

Let A be the event that the first mango is good and B denotes the event that the second is good.
Then,
$P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}$
$P(A\cap B)=\frac{{}^6{C}_2}{{}^{10}{C}_2}$
$P\left(A\right)=\frac{{}^6{C}_2}{{}^{10}{C}_2}+\frac{{}^6{C}_1{\times }^4{C}_1}{{}^{10}{C}_2}$
$\therefore P\left(\frac{B}{A}\right)=\frac{{}^6{C}_2}{{}^6{C}_2{+}^6{C}_1{\times }^4{C}_1}=\frac{5}{13}$