GATE 2025 DA – Question 31
There are three boxes containing white balls and black balls.
Box-1 contains 2 black and 1 white balls.
Box-2 contains 1 black and 2 white balls.
Box-3 contains 3 black and 3 white balls.
In a random experiment, one of these boxes is selected, where the probability of choosing Box-1 is $\frac{1}{2}$, Box-2 is $\frac{1}{6}$, and Box-3 is $\frac{1}{3}$. A ball is drawn at random from the selected box. Given that the ball drawn is white, the probability that it is drawn from Box-2 is ______ (*Round off to two decimal places*)
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Show answer and explanation
Correct answer: 0.24 to 0.26
Explanation
The chance of a white ball is $P(W) = \frac{1}{2} \cdot \frac{1}{3} + \frac{1}{6} \cdot \frac{2}{3} + \frac{1}{3} \cdot \frac{3}{6} = \frac{1}{6} + \frac{1}{9} + \frac{1}{6} = \frac{4}{9}$. By Bayes' theorem, $P(\text{Box-2} \mid W) = \frac{\frac{1}{6} \cdot \frac{2}{3}}{\frac{4}{9}} = \frac{1/9}{4/9} = 0.25$.