Twelve Zombies

12 zombies are in a room. 6 are green. 6 are blue.

Every minute they randomly form four groups of three. In any group, all three become the color of the majority (i.e. if two blue zombies and one green zombie are in a group, then they all become blue).

The expected number of minutes before all zombies are the same color can be written as \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is \(a+b\)?


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