Box A contains 4 red and 6 green balls. Box B contains 7 red and 3 green balls. A ball is drawn from box A and without seeing its colour, it is put into box B. If a ball is now drawn from box B, then the probability that it is red is:
Explanation:
Case 1: A red ball is transferred from A → B. P(red ball A → B) = 4/10 = 2/5 Now, box B has 8 red and 3 green balls. P(red ball is picked from B given that red A → B) = 8/11
∴ P(red ball is picked from B) = 2/5 × 8/11 = 16/55
Case 2: A green ball is transferred from A → B. P(green ball A → B) = 6/10 = 3/5 Now, box B has 7 red and 4 green balls. P(red ball is picked from B given that green A → B) = 7/11
∴ P(red ball is picked from B) = 3/5 × 7/11 = 21/55
⇒ P(red ball is picked from B) = 16/55 + 21/55 = 37/55
Hence, option (c).
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