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JEE MAIN 2025
22-01-2025 SHIFT-1
Question
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 :
Select the correct option:
A
4
B
14
C
13
D
11
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} & \mathrm{P}=\frac{\frac{6}{10} \times \frac{5}{9}}{\frac{4}{10} \times \frac{6}{9}+\frac{6}{10} \times \frac{5}{9}}=\frac{5}{9} \\ & \mathrm{~m}=5, \mathrm{n}=9 \\ & \mathrm{~m}+\mathrm{n}=14\end{aligned}$
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