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Bunuel
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Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
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It's really a conditional probability question, at least if I'm interpreting the wording correctly: knowing we have at least 2 red and at least 2 black marbles, what is the probability we have 3 of each? We can first count how many ways we might end up with 2 red and 4 black marbles. That's just like making a six-letter word using the letters R, R, B, B, B, B, which we can do in 6C2 ways (we're just choosing 2 of 6 positions in the word where we'll put the R's). Similarly there are 6C3 outcomes where we get 3 R's, and 6C4 outcomes where we get 4 R's. So there are 6C2 + 6C3 + 6C4 = 15 + 20 + 15 = 50 outcomes in total where we get at least 2 red and 2 black marbles, and of these, there are 6C3 = 20 where we get exactly 3 red and 3 black marbles, so the answer is 20/50 = 2/5.
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