JEE Main 2026 Jan 23 Shift 2, Mathematics Q11: Total Probability Theorem And Bayes' Theorem

JEE Main2026Jan 23, Shift 2Mathematics

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is $\frac{p}{q}$ , $g cd (p, q) = 1$ , then $p + q$ is equal to

A
22
B
23
C
24
D
21

Solution

Bag B has 10 balls: $P (white from B) = \frac{6}{10}$ , $P (black from B) = \frac{4}{10}$ .

After transfer, bag A has 18 balls.

If a white ball was moved: $P (white from A) = \frac{10}{18}$ .

If a black ball was moved: $P (white from A) = \frac{9}{18}$ .

Total probability:

$P = \frac{6}{10} \cdot \frac{10}{18} + \frac{4}{10} \cdot \frac{9}{18} = \frac{60 + 36}{180} = \frac{96}{180} = \frac{8}{15}$ .

With $p = 8$ , $q = 15$ : $p + q = 23$ .

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JEE Main 2026 Jan 23 Shift 2, Mathematics Q11: Total Probability Theorem And Bayes' Theorem

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