Mathematics · Probability

JEE Main 2025 — 22 January, Morning Shift — Question 19

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 $\frac{\mathrm{m}}{\mathrm{n}}$ , where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$ , then $\mathrm{m}+\mathrm{n}$ is equal to :

Option A:
14
Correct
Option B:
4
Option C:
11
Option D:
13

Answer: A

Step-by-step solution

$P=\frac{\frac{6}{10} \times \frac{5}{9}}{\frac{4}{10} \times \frac{6}{9}+\frac{6}{10} \times \frac{5}{9}}=\frac{5}{9}$

$\mathrm{m}=5, \mathrm{n}=9$

$\mathrm{m}+\mathrm{n}=14$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 22 January, Morning Shift
Subject: Mathematics
Chapter: Probability
Topic: Conditional Probability and Multiplication Theorem

A coin is tossed three times. Let X denote the number of times a tail follows a head. If mu and sigma^2 denote the mean and variance of X …

Answer: A

Step-by-step solution

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