Alan decides to use a different strategy for the 1-in-6 wins game of Exercise 90. He keeps buying one 20-ounce bottle of the soda at a time until he gets a winner.

a. Find the probability that he buys exactly 5 bottles.

b. Find the probability that he buys at most 6 bottles. Show your work.

Exercise 90.

As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each bottle cap. Some of the caps said, “Please try again!” while others said, “You’re a winner!” The company advertised the promotion with the slogan “1 in 6 wins a prize.” Grayson’s statistics class wonders if the company’s claim holds true at a nearby convenience store. To find out, all 30 students in the class go to the store and each buys one 20-ounce bottle of the soda.