As a special promotion for its 20-ounce bottles of soda, a softdrink company printed a message on the inside of each cap. Some ofthe caps said, “Please try again,†while others said, “You’re awinner!†The company advertised the promotion with the slogan “1 in6 wins a prize.†Suppose the company is telling the truth and thatevery 20-ounce bottle of soda it fills has a 1-in-6 chance of beinga winner. Seven friends each buy one 20-ounce bottle of the soda ata local convenience store. Let X = the number who win a prize. Theprobability distribution of X is shown here.
a)The store clerk is surprised when 3 of the friends win aprize. Is this group of friends just lucky, or is the company’s1-in-6 claim inaccurate? Find the probability that at least 3 of agroup of 7 friends would win a prize and use the result to justifyyour answer.
Winners | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Probability | 0.2791 | 0.3907 | 0.2344 | 0.0781 | 0.0156 | 0.0019 | 0.0001 | 0.000004 |
