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

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$\frac{5}{13}$

$\frac{1}{5}$

$\frac{2}{3}$

$\frac{8}{13}$

answer is A.

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Detailed Solution

$A = O n e o f t h e m i s g o o d n (A) = {}^{4}C_{1} \times {}^{6}C_{1} + {}^{6}C_{2} B = both are good P (A \cap B) = {}^{6}C_{2} P (B / A) = \frac{P (A \cap B)}{P (A)} = \frac{{}^{6}C_{2}}{{}^{4}C_{1} \times {}^{6}C_{1} + {}^{6}C_{2}} = \frac{5}{13}$

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