Q28 / 75 · JEE Main 2025 (22 Jan Shift 1) · Mathematics

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 ball is black, given that the second selected ball is also black, is $\frac{m}{n}$, where $\operatorname{gcd}(m, n)=1$, then $m+n$ is equal to :

  • A
    $4$
  • Correct answer
    B
    $14$
  • C
    $13$
  • D
    $11$

Solution

Bag contains 4 white and 6 black balls $A$ : first ball selected is black $B$ : Second ball is also black $\begin{aligned} & P\left(\frac{A}{B}\right)=\frac{\frac{6}{10} \times \frac{5}{9}}{\frac{4}{10} \times \frac{6}{9}+\frac{6}{10} \times \frac{5}{9}}=\frac{30}{24+30} \\ & =\frac{30}{54}=\frac{5}{9} \\ & m+n=5+9=14 \end{aligned}$

Hence, the correct answer is option: 'B'.

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