Question

A box contains $10$ mangoes out of which $4$ are spoiled. $2$ mangoes are taken together at random. If one of them is found to be good, then the probability that the other is also good, is

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{8}{15}$
• D. $\frac{5}{13}$

Answer 1

Answer: (D)

Let $A$ be the event that the first mango is good and $B$ be the event that second is good.
$\therefore$ Required probability $=P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P(A)}$
$P(A)=\frac{{}^6{C}_2}{{}^{10}{C}_2}+\frac{{}^6{C}_1\times {}^4{C}_1}{{}^{10}{C}_2}$
$P(A\cap B)=\frac{{}^6{C}_2}{{}^{10}{C}_2}$
$\therefore P\left(\frac{B}{A}\right)=\frac{{}^6{C}_2}{{}^6{C}_2+{}^6{C}_1\times {}^4{C}_1}=\frac{15}{15+24}=\frac{15}{39}=\frac{5}{13}$