examday

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Newton has a wardrobe containing $7$ hats of $3$ different types: $3$ Einstein hats, $2$ Euler hats, and $2$ Newton hats. He repeatedly takes out $2$ hats at a time from the wardrobe at random, and stops if the two hats are of the same type. However, Newton is “Einstein-Euler type-blind”, so he also stops if he takes out one Einstein hat and one Euler hat. What is the probability that he stops with $2$ hats of the same type? Assume he returns both hats to the wardrobe after each step.