A bag contains 3 red and 2 black ball. Another bag contains 4 red and 5 black balls. A ball is drawn from the first bag and is placed in the second. A ball is then drawn from the second. What is the probability that this draw of red ball is due to the drawing of red ball from the first bag ?\nOptions:\n(A) 3/5\n(B) 2/5\n(C) 4/25\n(D) 3/10\n(E) 15/23 Think first, then make a decision. Some random thoughts:
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Probability of getting red ball from bag1 and then red from bag 2 = 3/5*5/10 = 15/50\nProbability of getting black ball from bag1 and then red from bag 2 = 2/5*4/10 = 8/50\nNow comes the condition, hence apply conditional probability:\nP(Red)/ P(Red + Black)\n(15/50)/(15/50+8/50) = 15/50 /23/50 = 15/23. So the answer is (E).
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