Question One: The local cafe is open 7 days a week and has a newbie barista working 2 days a week, and an expert barista working 5 days a week. (The days are chosen randomly without a specific order, and only one barista is on duty at any one time). The newbie barista makes an excellent coffee with probability 20% and a good coffee with probability 80%. The expert barista makes an excellent coffee with probability 95% and a good coffee with probability 5%. (a) What is the probability of getting a good coffee on any given day? (b) Given that you got a good coffee, what is the probability that the expert barista is on duty today? (c) Given that you got a good coffee, what's the probability that the next coffee is going to be excellent? (d) After how many good coffees in a row would you be at least 98% certain that a newbie barista is on duty today?