What is the probability that each of the 15 customers is able to purchase the type of drink desired?

Question

A soft-drink machine dispenses only regular Pepsi and Diet Pepsi. Sixty percent of all the purchases from this
machine are diet drinks. The machine currently has 10 cans of each type of soda. Assume that every customer’s
preferred soft drink is independent from all other customers; therefore, we have a binomial distribution. If 15 customers
want to purchase drinks before the machine is restocked, what is the probability that each of the 15 customers is able to
purchase the type of drink desired? (Hint: Let x be the number among the 15 who want a diet drink, and the probability
of success in one trial is 0.6.)

Answer 1

Hi Julia,

If x is the number of people who  want diet soda

Probability that each customer is satisfied with their option = ¹⁵C_x (0.6)^x(0.4)^15-x

                                                                                  = [15!/x!(15-x)!](0.6)^x(0.4)^15-x