JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Probability

Bag

B_{1}

contains 6 white and 4 blue balls, Bag

B_{2}

contains 4 white and 6 blue balls, and

Bag B_{3}

contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that the ball is drawn from

Bag_{2}

, is :

(A) $\frac{1}{3}$
(B) $\frac{4}{15}$ ✓ Correct
(C) $\frac{2}{3}$
(D) $\frac{2}{5}$

Answer: (B)

Solution

Let

E_{1}, E_{2}, E_{3}

be the events of choosing bags

B_{1}, B_{2}, B_{3}

, each with probability

\frac{1}{3}

, and let

W

be the event of drawing a white ball.

P (W ∣ E_{1}) = \frac{6}{10}, P (W ∣ E_{2}) = \frac{4}{10}, P (W ∣ E_{3}) = \frac{5}{10}

By Bayes' theorem,

P (E_{2} ∣ W) = \frac{\frac{1}{3} \cdot \frac{4}{10}}{\frac{1}{3} \cdot \frac{6}{10} + \frac{1}{3} \cdot \frac{4}{10} + \frac{1}{3} \cdot \frac{5}{10}} = \frac{4}{6 + 4 + 5} = \frac{4}{15}

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Single correct option

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JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Probability

Solution

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