According to results from the Spine Patient Outcomes Research Trial, or SPORT, surgery for a painful, common back condition resulted in significantly reduced back pain and better physical function than treatment with drugs and physical therapy (The W a ll S tre e t J o u rn a l, February 21, 2008).

SPORT followed 803 patients, of whom 398 ended up getting surgery. After two years, of those who had surgery, 63% 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? What is the probability that a patient did not have surgery?

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

c. What is the probability that a patient received nonsurgical treatment and experienced a major improvement in his or her condition?  P-258