Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected balls is black, given that the second selected ball is also black is , where gcd (m, n) = 1, then m

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Solution

Q.
Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected balls is black, given that the second selected ball is also black is $\frac{m}{n}$ , where gcd (m, n) = 1, then m + n is equal to : [2025]

1 11

2 13

3 4

4 14

Ans.
(4)

Required probability

$= \frac{\frac{6}{10} \times \frac{5}{9}}{\frac{4}{10} \times \frac{6}{9} + \frac{6}{10} \times \frac{5}{9}} = \frac{30}{24 + 30} = \frac{30}{54} = \frac{5}{9}$

So, m = 5, n = 9 [ $∵$ gcd (m, n) = 1]

$∴$ m + n = 14.

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