3. Assume that 59% of all customers will take free samples. Furthermore, of those who take the free samples, assume that about 32% will buy what they have sampled. Suppose that you set up a counter in a supermarket offering free samples of a new product and that the day you were offering free samples, 274 customers passed by your counter. 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 we are given the conditional probability P(buy, given sample) = 0.32, while P(sample) = 0.59.] Page 1 4. Suppose that more than a decade ago high levels of lead in the blood put 83% of children at risk. A concerted effort was made to remove lead from the environment. Suppose, according to a survey, only 7% of children in the United States are at risk of high blood-lead levels. In a random sample of 300 children taken more than a decade ago, what is the probability that 230 or more had high blood-lead levels? 5. Suppose that about 57% of the people who are murdered actually knew the person who committed the murder. Suppose that a detective file in Boston has 66 current unsolved murders. What is the probability that fewer than 34 victims did not know their murderer?