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In one urn, put the one white marble and one green marble; in the other urn put the rest. Then the two marbles drawn from the first urn will be one white and one green with 100% probability, so we consider the second urn which contains 13 marbles. There 13 possible choices for the first marble drawn, and 12 possible choices for the second marble, and it makes no difference in what order we draw them: so there are 12x13/2 or 78 possible pairs (13 choose 2). To end up with four differently-colored marbles, we must get either a red and a yellow (2x3 = 6 possible pairs), a red and a blue (2x4 = 8 possible pairs), or a yellow and a blue (3x4 = 12 possible pairs), so there are 6+8+12 = 26 possible ways to get four differently-colored marbles. This gives us a probability of 26/78 = 1/3. |
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