Question Answered step-by-step Question 1: Suppose that, based on past weather data, during the… Question 1: Suppose that, based on past weather data, during the month of April in Winnipeg, on any given day, it rains (R) with probability 0.40, there is a snow fall (F ) with probability 0.45 and it is dry (D) with probability 0.15. Assume there is only one type of weather each day and that each day’s weather are independent. Suppose I record the weather on two days in April.(a) Write out the sample space.(b) Let A be the event it snows on the first day. Let B be the event it rains on the second day. Find AB.Are A and B independent? If so, justify mathematically.(c) Let X denote the number of days it rains amongst the two days. Write out the probability distributionof X. Question 3: Suppose a professor teaches a class daily (Monday-Friday). He has a tendency to be late for his daily lectures with probability 0.68. Assume that the professor’s punctuality on each day is independent.(a) What is the probability that he is not late to any of his lectures?(b) What is the probability that he is late to at least four of his lectures?(c) What is the mean number of days he is late during one week of classes? Math Statistics and Probability STAT 2023 Share QuestionEmailCopy link Comments (0)