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GATE DA 2025 Q31: Bayes' theorem: white ball came from Box-2

Question

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 12\frac{1}{2}, Box-2 is 16\frac{1}{6}, and Box-3 is 13\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)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 0.25 (official GATE 2025 final answer key)

Concept used: Bayes' theorem with the law of total probability.

First step: First find P(white)=12⋅13+16⋅23+13⋅12P(\text{white}) = \frac{1}{2} \cdot \frac{1}{3} + \frac{1}{6} \cdot \frac{2}{3} + \frac{1}{3} \cdot \frac{1}{2}, then divide the Box-2 term by it.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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