# Three Marbles in Pólya's Urn

**Discrete Mathematics**Level 5

You have an urn with three marbles in it, a red one a yellow one and a blue one. Every ten seconds you pull out one marble at random and replace it together with one of the same color. e.g. If you pick out a red marble, you will replace it with two red marbles.

So, now the question...

The probability that at some point you will have 8 red marbles, 12 yellow marbles, and 3 blue ones after the corresponding number of moves is \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers.

What is \(a + b\)?

**Image credit:** www.funeral-urn.com

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