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3. Steve, a student at SISU, has illegally parked his car in the employee parking lot. If Robert the ticket- writer is on duty there's a 90% chance that Steve will get a ticket because of Robert's vigilance. If any other ticket-writer is on duty, there's only a 50% chance that Steve will get a ticket. Steve doesn't know which ticket-writer is on duty, but there's a 30% chance that it is Robert. Show all the steps including identification of what formulas/properties you used. Points will be deducted from answers if only the final answer is provided. (a) Define events that would be useful in analyzing this situation. (b) Write out mathematically the probabilities that are provided as well as inferred (their complements.) (c) If Robert is on duty, what is the probability that Steve does not get a ticket? (d) Using common sense, is the probability that Steve gets a ticket closer to 50% or 90%? e) Calculate the probability that Steve gets a ticket. (f) it turns out that Steve was lucky and did not get a ticket. What is the probability that Robert was the ticket-writer on duty