1.According to results from a research trial for a painful, shoulder condition resulted in reduced pain and better physical function than treatment with just physical therapy. Researchers followed 803 patients, of whom 398 ended up getting surgery. After two years, of those who had surgery, 63% percent said they had a major improvement in their condition, compared with 29% among those who received nonsurgical treatment.

a.What is the probability that a patient had surgery?

b.What is the probability that a patient did not have surgery?

c.What is the probability that a patient had surgery and experienced a major improvement in his or her condition?

d.What is the probability that a patient received nonsurgical treatment and experience a major improvement in his or her condition?

2.Suppose that 45 percent of a company's batteries are manufactured in Factory A, while 55 percent are manufactured in Factory B. The defect rates for the two factories are 35 percent for Factory A and 25 percent for Factory B. Suppose that we have a defective battery.

a.Find the probability that the defective battery was manufactured by Factory A.

b.If the company that you were advising asked you to recommend a factory purchase their batteries from what factory would you recommend? (Factory A or Factory B).

c.Why would you make that recommendation?

3.You financial firm has 12 possible funds in which to invest, but you are only allowed to market 5 funds to your costumers during the first quarter. How many possible combinations of the 12 funds are there for you to choose from?

4.There are three empty seats at a concert, but ten people showed up to try to get one of those three seats. If three people are picked at random to get the last three seats, what is the probability you and your two friends will get the tickets?