Question: You are taking a multiple-choice test which has 20 questions. Each question has five possible answers, only one of which is correct. You guess the

You are taking a multiple-choice test which has 20 questions. Each question has five possible answers, only one of which is correct. You guess the answer for every question by rolling a fair five-sided die. Let X be the number of questions you get correct in the whole test and let Y be the number of questions you get correct among the first 15 questions

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