GATE 2026 CE (CE1) – Question 26
Bag I contains 4 white and 6 black balls.
Bag II contains 4 white and 3 black balls.
One ball is drawn at random from any one of the two bags and it is found to be a black ball. The probability that the black ball was drawn from Bag I is ______ (*rounded off to two decimal places*).
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Correct answer: 0.57 to 0.59
Explanation
Each bag is chosen with probability $\frac{1}{2}$. The probability of black from Bag I is $\frac{6}{10}$ and from Bag II it is $\frac{3}{7}$. By Bayes' theorem, $\frac{0.5 \times 0.6}{0.5 \times 0.6 + 0.5 \times \frac{3}{7}} = \frac{0.3}{0.5143} = 0.58$.