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Q.

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

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a

$\frac{5}{13}$

b

$\frac{2}{3}$

c

$\frac{8}{15}$

d

$\frac{1}{3}$

answer is D.

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Detailed Solution

Let A is the event first mango is good , $P (A) = \frac{6 C_{2} + 6 C_{1} \times 4 C_{1}}{10 C_{2}}$
Let B is the event second mango is good,
$\begin{array}{l} P (A \cap B) = \frac{6 C_{2}}{10 C_{2}} \\ ∴ P (\frac{B}{A}) = \frac{P (A \cap B)}{P (A)} = \frac{6 C_{2}}{6 C_{2} + 6 C_{1} \times 4 C_{1}} = \frac{5}{13} \end{array}$

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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