# Collect all three!

You play a new online game called, "Pokey Mango!" It's a game where you go around collecting strange cartoonish beasts.

Suppose there are only three such beasts in the game, and each beast has the following probability of being found:

• Snorlax $$\frac{1}{6}$$
• Drowzee $$\frac{1}{3}$$
• Magikarp $$\frac{1}{2}$$

The expected total number of beasts you need to collect before you have "Collected them All" (In this case there are only $$3$$) is $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. What is $$a+ b$$?

Image credit: http://forums.smitegame.com/ , http://nintendo.wikia.com/ , http://www.dltk-kids.com/

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