In 2018, Tim Hortons® restaurants conducted a game called Roll up the Rim to Win® where you could roll up the rim of one of their medium-sized or larger beverage paper cups (to reveal something underneath) and possibly win a prize. About 1/6 of the cups were winners. The prizes mostly consisted of a free coffee or donut. 

a. If you buy 3 beverages sold in these cups, what is the probability that you will have exactly one winner? 

b. If you buy 3 beverages sold in these cups, what is the probability that you will have at least one winner? 

c. Suppose you plan to keep buying beverages until you get a winner. What is the probability that you will have to buy 3 beverages until you get a winner? 

d. Suppose you plan to keep buying beverages until you get a winner. What is the probability that you will have to buy 3 or fewer beverages until you get a winner?