A box contains 10 mangoes out of which 4 are rotten. 2 mangoes are taken out together. If one of the

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14.Probability

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

A

$\frac{1}{3}$

B

$\frac{8}{{15}}$

C

$\frac{5}{{18}}$

D

$\frac{2}{3}$

Solution

(c) Number of ways of selecting two good mangoes $= $$^6{C_2} = 15$.

Number of ways that at least one of the two selected mangoes is to be good $ = {}^6{C_1} \times {}^9{C_1} = 54$

$\therefore $ Required probability $ = \frac{{15}}{{64}} = \frac{5}{{18}}$.

Standard 11

Mathematics

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