Question 2 (30 points): Choosing the right discrete distribution Medipol’s Polin Cafe distributes a coupon whenever a students buys a coffee. There are three types of coupons: ’2 free coffees’, ’1 free coffee’, and ’Buy again’ coupons. The coupons are randomly placed in a coupon box, and the cashier randomly chooses one. The probability of getting ’2 free coffee’ coupon is c1/100, while the probability of ’1 free coffee’ coupon is c4/100. (a) (5 Pts.) Assume that a student bought c4 coffees. What is the probability that he got any of the free coffee coupons more than 3 times? (b) (5 Pts.) On average how many coffees a student need to buy in order to get either of the free coffee coupons? (c) (5 Pts.) One of the students says that if he/she does not get any of the free coffee coupon after he buys his 10th coffee, he will then stop buying coffee from Polin Cafe. What is the probability that this event happening? (d) (5 Pts.) On average, how many coffees a student need to buy in order to get his first ’2 free coffee’ coupon? (e) (5 Pts.) We met 10 students who purchased c2 coffees. What is the probability that at least 2 of these students got either of the free coffee coupons? (f) (5 Pts.) For the previous part, we take c1 students out of the 10 students. What is probability that we have at least 1 student who did not get any free coupons at all? c1= 4 , c4 = 10