1.Two basketball players are very different when it comes to making free throws. Justin makes70% of his free throw shots while Mark makes65% of his free throws. Assume that the free throws are independent and that each player shoots two free throws during a team practice.

(a) What is the probability that Justin makes both of his free throws?

(b) What is the probability that Mark makes exactly one of his two free throws?

(c) What is the probability that Justin makes both of his free throws and Mark makes neither of his? (Round your answer to four decimal places.)

2.To reduce the cost of detecting a disease, blood tests are conducted on a pooled sample of blood collected from a group ofnpeople. If no indication of the disease is present in the pooled blood sample, none have the disease. If analysis of the pooled blood sample indicates that the disease is present, the blood of each individual must be tested. The individual tests are conducted in sequence. If, among a group ofeightpeople, one person has the disease, what is the probability thatnineblood tests (including the pooled test) are required to detect the single diseased person? (Enter your probability as a fraction.)

If two people have the disease, what is the probability thatninetests are required to locate both diseased people? (Assume the last two tests are given to the diseased people. Enter your probability as a fraction.)