Class JEE Mathematics Statistics and Probability Q #990
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4 Marks 2025 JEE Main 2025 (Online) 28th January Evening Shift MCQ SINGLE
Bag $B_1$ contains 6 white and 4 blue balls, Bag $B_2$ contains 4 white and 6 blue balls, and Bag $B_3$ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability that the ball is drawn from Bag $B_2$ is:
(A) $\frac{2}{5}$
(B) $\frac{4}{15}$
(C) $\frac{1}{3}$
(D) $\frac{2}{3}$
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Correct Answer: B
Explanation
$E_1$: Bag $B_1$ is selected
$B_1$: 6 W 4 B
$B_2$: 4 W 6 B
$B_3$: 5 W 5 B
$E_2$: bag $B_2$ is selected
We have to find $P(\frac{E_2}{A})$
$P(\frac{E_2}{A}) = \frac{P(E_2)P(\frac{A}{E_2})}{P(E_1)P(\frac{A}{E_1}) + P(E_2)P(\frac{A}{E_2}) + P(E_3)P(\frac{A}{E_3})} = \frac{\frac{1}{3} \times \frac{4}{10}}{\frac{1}{3} \times \frac{6}{10} + \frac{1}{3} \times \frac{4}{10} + \frac{1}{3} \times \frac{5}{10}} = \frac{4}{15}$

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