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(5) Janice is a very superstitious chess player. She believes that the hat she wears has an impact
on whether she wins, loses, or stalemates a game. Let X be the type of hat she wears and Y be
the outcome of the game. The joint probability distribution is provided below. (a) In a couple
sentences, describe what is slightly different about this situation than most of the problems we
have discussed thus far. Hint: think about the values that the two random variables can take. (b) Is
Janice's superstition justified? Explain, with appropriate mathematical justification, why or why not.

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