OK, man, GO!

Discrete Mathematics Level 4

Every day Crazy Jake wanders randomly from his countryside cottage. \(\dfrac{2}{3}\) of the time he ends up in the desert, and \(\dfrac{1}{3}\) of the time he ends up at the beach.

When he gets to his destination he plays an obscure little game on his phone called "OK, man, GO!". This is a game where he hunts for little cartoonish creatures.

Now, if he's at the beach, each creature he finds has an 80% chance of being a Magikarp. If he's in the desert, each creature he finds has only a 10% chance of being the Magikarp.

Got it?

So now for the question...

If he goes about on his journey one day, and when he gets there he only finds two creatures and they are both Magikarp, what is the probability he is at the beach?

Round your answer to 2 decimal places.

Image credit: hoopa-u.tumblr.com

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