Do you take the free samples offered in supermarkets? About 62% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled....

Do you take the free samples offered in supermarkets? About 62% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 315 customers passed by your counter. (Round your answers to four decimal places.)

(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for
dependent
events. Notice that we are given the conditional probability
P(buy|sample) = 0.37, while
P(sample) = 0.62.

(d) What is the probability that between 60 and 80 customers will take the free sample

and

buy the product?
Hint:
Use the probability of success calculated in part (c).