Surgery for a painful, common back condition often results in significantly reduced back pain and better physical function than treatment with drugs and physical therapy. A researcher 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-1. What is the probability that a patient had surgery? (Round your answer to 4 decimal places.)        a-2. What is the probability that a patient did not have surgery? (Round your answer to 4 decimal places.)

Surgery for a painful, common back condition often results in significantly reduced back pain and better physical function than treatment with drugs and physical therapy. A researcher 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-1. What is the probability that a patient had surgery? (Round your answer to 4 decimal places.)
  

 
a-2. What is the probability that a patient did not have surgery? (Round your answer to 4 decimal places.)
  

 
b. What is the probability that a patient had surgery and experienced a major improvement in his or her condition? (Round your answer to 4 decimal places.)
  

 
c. What is the probability that a patient received nonsurgical treatment and experienced a major improvement in his or her condition? (Round your answer to 4 decimal places.)
  

rev: 08_24_2021_QC_CS-273373