GATE CE 2026 Set 1 — Question 26
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Engineering Mathematics → Probability → Bayes' Theorem
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Question
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).
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).
Correct answer
0.5 to 0.66
Solution
Let be the event of choosing Bag I and be the event of choosing Bag II. Since the bag is chosen at random, .
Let be the event of drawing a black ball.
From Bag I:
From Bag II:
Using Bayes' Theorem, the probability that the black ball was drawn from Bag I is:Rounding off to two decimal places, we get 0.58.
Let be the event of drawing a black ball.
From Bag I:
From Bag II:
Using Bayes' Theorem, the probability that the black ball was drawn from Bag I is:Rounding off to two decimal places, we get 0.58.
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