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1. A bag contains 10 mangoes out of which 4 are rotten, two mangoes are taken out together. If one of them is found to be good, the probability that other also good is-

A. $\frac{1}{3}$

B. $\frac{8}{15}$

C. $\frac{5}{18}$

D. $\frac{2}{3}$

Solution:

Out of mangoes, 4 mangoes are rotten
∴ Required probability

\begin{aligned} = \frac{^{6} C_{2}}{^{10} C_{2}} \\ = \frac{\frac{6!}{2! (6 - 2)!}}{\frac{10!}{2! (10 - 2)!}} \\ = \frac{\frac{6!}{2! 4!}}{\frac{10!}{2! \times 8!}} \\ = \frac{\frac{6 \times 5}{1 \times 2}}{\frac{10 \times 9}{1 \times 2}} \\ = \frac{6 \times 5}{10 \times 9} \\ = \frac{1}{3} \end{aligned}

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