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Finding Nemo

Nemo is playing hide-and-seek with his forgetful fish friend. There are three reefs that Nemo can hide in. Nemo decides to hide in Reef A. The game begins …
Being a forgetful fish, if she doesn’t find Nemo, she will swim out and totally forget which reef she was just in! (Meaning she can go into the same reef over and over again). If Nemo’s friend randomly selects a reef to search at each turn (with equal chance), and continues until she finds him, what is the expected length of the game?
How long, on average, does it take to find Nemo?