Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is p q , gcd ( p , q )=1, then p + q is equal to
A. 23
Bag A: 9W, 8B. Bag B: 6W, 4B. Case 1: White transferred from B (prob = 6 10 ). A becomes 10W, 8B. P( white from A ) = 10 18 = 5 9 . Case 2: Black transferred from B (prob = 4 10 ). A becomes 9W, 9B. P( white from A ) = 9 18 = 1 2 . Total probability = 6 10 5 9 + 4 10 1 2 = 1 3 + 1 5 = 8 15 . p = 8, q = 15, (8,15) = 1. So p + q = 23.
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