(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..