JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Probability

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Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is :

(A) $\frac{5}{18}$ ✓ Correct
(B) $\frac{5}{16}$
(C) $\frac{4}{17}$
(D) $\frac{7}{18}$

Answer: (A)

Solution

Prior

P (A) = P (B) = P (C) = \frac{1}{3}

. Probability of drawing black:

P (bl ∣ A) = \frac{5}{12}, P (bl ∣ B) = \frac{7}{12}, P (bl ∣ C) = \frac{6}{12} .

By Bayes,

P (A ∣ bl) = \frac{\frac{1}{3} \cdot \frac{5}{12}}{\frac{1}{3} ( \frac{5}{12} + \frac{7}{12} + \frac{6}{12} )} = \frac{5}{18} .

Option A.

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Single correct option

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