249.Flipping Two Balls at a Time
★★★markov chainsJump Trading
A bag holds 4 balls: 2 black and 2 white. You pick two balls at random and invert the colour of each (black becomes white and white becomes black), then return them. You repeat until all four balls are the same colour. What is the expected number of operations?
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Work out what each of the three possible picks does to the colour split. Two of them finish the job immediately.
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