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Instructions ' Please answer each of the following questions In order. There are four questions in total. You may write your answers neatly by hand or type them up, or a mix of the two. You will need to submit your assignment as a PDF le. You can use your phone to scan written work and convert to PDF. You may use any software or technology to answer the questions below. You may also work by hand. l recommend (but do not require] that you use Microsoft Excel.' Y0ur assignment must be submitted on Moodle. Emailed submissions will not be accepted. 1. Event A has probability 0.5 and event 8 has probability ()2. Further, PMJBJ = 0.6. Answer each of the below. and support your answer with calculations. 3 Find PM AND B). b. Are A and 8 independent? How do you know? c. Are A and B mutually exclusive? How do you know? d. Find Pm OR B). e. Find P(BIA). 2 Sabine loves to go out for coffee on weekdays. She always goes at least once, and never goes more than five times in a week. She goes out for coffee five times a week on average 30% of the time, four times a week 32% of the time, three times a week 20% of the time. and twice a week 11% of the ttme 3. Define the random variable X that corresponds to the scenario above. b What values does I take on? c, Construct a PDF table. [1 Find the probability that Sabine gets coffee at least 3 times a week