Will there still be blue and green when the reds run out?

Question

A jar contains 10 red, 20 blue and 30 green candies. You take them out one at a time, uniformly at random, until the jar is empty. What is the probability that, at the moment the last red candy is removed, there is still at least one blue candy and at least one green candy in the jar?

Accepted Answer

7/12. Reformulate. We want the event that red runs out before both blue and green. Its complement is: blue runs out before red, or green runs out before red. Colour drawn last within a group. Ignore all other colours and look only at the reds and blues: the order in which those 30 candies come out is a uniformly random order, so the last of them is red with probability 10/30 = 1/3. "The last of the reds-and-blues is red" is exactly "blue runs out before red". Likewise, among reds and greens, the last is red with probability 10/40 = 1/4, which is "green runs out before red". And among all 60 c…

Will there still be blue and green when the reds run out?

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