medium Probability
A release-checked medium problem for training Law of Total Probability, Conditional Probability.
Beth has $r$ red marbles, $b$ blue marbles, and $g$ green marbles in an urn. She draws out the marbles one at a time without replacement. Find the probability there is at least one green and one blue marble left in the urn right after the last red marble is selected. Find this probability when $r = 10, b = 20, g = 30$.
This Probability problem is tagged Law of Total Probability, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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