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.

a. Find the probability that two or fewer students would win a prize if the company’s claim is true.

b. Two of the students in Grayson’s class got caps that say, “You’re a winner!” Does this result give convincing evidence that the company’s 1-in-6 claim is false?