A bag contains 15 red balls and 20 black balls. Each ball is numbered either 1 or 2 or 3. 20% of the red balls are numbered 1 and 40% of them are numbered 3. Similarly, among the black balls, 45% are numbered 2 and 30% are numbered 3. A boy picks a ball at random. He wins if the ball is red and numbered 3 or if it is black and numbered 1 or 2. What are the chances of his winning?
1/2
4/7
5/9
12 /13
Probability of picking a random ball is Red → 15/35, [ within the 15 red balls : Red with number 1 → 20% of 15 = 3/15, Red with number 3 → 40% of 15 = 6/15 ]. Black → 20/35, [ within the 20 black balls : Black with number 2 = 45% of 20 = 9/20, Black with number 3 = 30% of 20 = 6/20 ]. So, we have to find probability of red balls with number 3 or black balls with numbers 1 and 2 So probability is
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