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 Wall Street Journal, February 21, 2008).
SPORT followed 803 patients, of who 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?