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 \(a+ b\)?

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