Question

A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken together. If one of them is found to be good, the probability that the other is rotten is

• A. $\frac{5}{13}$
• B. $\frac{7}{13}$
• C. $\frac{8}{15}$
• D. $\frac{9}{13}$

Answer 1

The correct option is C $\frac{8}{15}$

A box contains 10 mangoes out of which 4 are rotten.
Probability of taking one rotten mango $=\frac{4}{10}=\frac{2}{5}$
Probability of taking one good mango $=\frac{6}{10}=\frac{3}{5}$
If one of them is found to be good, the probability that the other is rotten is then first one is good and second is rotten or first one is rotten and second one is good $=\frac{6}{10}\times \frac{4}{9}+\frac{4}{10}\times \frac{6}{9}=\frac{48}{90}=\frac{8}{15}$