7. Professor May B. Right often has her science facts wrong, and answers each of her...

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7. Professor May B. Right often has her science facts wrong, and answers each of her students questions incorrectly with probability 1/4, independently of other questions. In each lecture May is asked either 1 or 2 questions with equal probability. a. Let A be the event that May gives wrong answers to all the questions she gets in a given lecture. Find P(A). b. Let B be the event that May gave wrong answers to all the questions she got in a given lecture, and let C be the event that she got two questions. Find P(C|B). c. Let X and Y be the number of questions May gets and the number of questions she answers correctly in a lecture respectively. Find the pmf of Y 7. Professor May B. Right often has her science facts wrong, and answers each of her students questions incorrectly with probability 1/4, independently of other questions. In each lecture May is asked either 1 or 2 questions with equal probability. a. Let A be the event that May gives wrong answers to all the questions she gets in a given lecture. Find P(A). b. Let B be the event that May gave wrong answers to all the questions she got in a given lecture, and let C be the event that she got two questions. Find P(C|B). c. Let X and Y be the number of questions May gets and the number of questions she answers correctly in a lecture respectively. Find the pmf of Y