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Probability
RS Aggarwal
CBSE
Grade 12
Question:
Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in color. Find the probability that the transferred ball was black.
Step-by-Step Solution
Key Concept: Let E1: transferred ball is red (3/7), E2: transferred ball is black (4/7). A: ball drawn from Bag II is red. P(A|E1) = 5/10 = 1/2. P(A|E2) = 4/10 = 2/5. By Bayes Theorem: P(E2|A) = (4/7 * 2/5) / (3/7 * 1/2 + 4/7 * 2/5) = (8/35) / (15/70 + 16/70) = (16/70) / (31/70) = 16/31.
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