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Probability
Bayes' Theorem
jee_main_2026_april_5_shift_1
Grade 12
Question:
There are two bags: Bag A contains 4 white and 2 black balls, Bag B contains 1 white and 2 black balls. One bag is chosen at random and a ball is drawn. If the drawn ball is white, find the probability that it came from Bag A.
A. 1/4
B. 1/3
C. 1/2
D. 2/3
Step-by-Step Solution
Key Concept: Use Bayes' theorem with prior probabilities equal.
Step 1: P(Bag A) = P(Bag B) = 1/2. Step 2: P(White | Bag A) = 4/6 = 2/3. Step 3: P(White | Bag B) = 1/3. Step 4: P(Bag A | White) = (1/2 × 2/3) / (1/2 × 2/3 + 1/2 × 1/3) = (1/3) / (1/3 + 1/6) = (1/3) / (2/6 + 1/6) = (1/3) / (3/6) = (1/3) / (1/2) = 2/3.
Correct Answer:D
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