Answer to Question #309690 in Statistics and Probability for sohyun

Question

The most dangerous aspect of the procedure is the possibility that the body may reject the new organ. Several new drugs are available for such circumstances, and the earlier the drug is administered, the higher the probability of averting rejection. The Journal recently reported the development of a new urine test to detect early warning signs that the body is rejecting a transplanted kidney. However, like most other tests, the new test is not perfect. When the test is conducted on someone whose kidney will be rejected, approximately one out of five tests will be negative (i.e., the test is wrong). When the test is conducted on a person whose kidney will not be rejected, 8% will show a positive test result (i.e., another incorrect result). Physicians know that in about 35% of kidney transplants the body tries to reject the organ. Suppose that the test was performed and the test is positive (indicating early warning of rejection). What is the probability that the body is attempting to reject the kidney?