# Collect all three!

**Discrete Mathematics**Level 4

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/