You have the best roommate ever. Each weekend day (Saturdays and Sundays) there is a 25% chance that they will go pick up bagels and coee before you wake up. Each weekday (Monday-Friday) there is a 10% chance that they will go pick up bagels and coee before you get up. (a) You wake up in the morning from a deep sleep and you have no idea what day of the week it is. It could be any of the seven days of the week with equal probability. What is the probability that your roommate has gotten you bagels and coee? (b) Suppose your roommate has bought you bagels and coee, what is the probability it is the weekend (Saturday or Sunday)? (c) Let B be the number of days you get bagels and coee from your roommate over the next 14 days (4 weekend days and 10 weekday days). Find E[B] and V ar(B). (d) Find P (B = 1) (e) If you only get bagels once over the next 14 days, what is the probability it was a weekend day?