JEE Main 2025 — Probability Question with Solution
JEE Main 2025 (22 Jan 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 , where , then is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
Bag contains 4 white and 6 black balls
: first ball selected is black
: Second ball is also black
$\begin{aligned}
& P\left(\frac{A}{B}\right)=\frac{\frac{6}{10} \times \frac{5}{9}}{\frac{4}{10} \times \frac{6}{9}+\frac{6}{10} \times \frac{5}{9}}=\frac{30}{24+30} \\
& =\frac{30}{54}=\frac{5}{9} \\
& m+n=5+9=14
\end{aligned}$
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This is a previous-year question from JEE Main 2025, covering the Probability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.