Given positive test, find probability that transplanted kidney is being rejected

Transplant operations have become routine. One common transplant operation is for kidneys. The most dangerous aspect of the procedure is the possibility that the body may reject the new organ. There are several new drugs available for such circumstances and the earlier the drug is administered, the higher the probability of averting rejection.

The New England Journal of Medicine 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. In fact, 20% of positive tests (kidneys are being rejected) and 8% of negative tests (kidneys are NOT being rejected) prove to be incorrect. Physicians know that in about 33% of kidney transplants the body tries to reject the organ.

If the new test has a positive result (indicating early warning of rejection), what is the probability that the body is attempting to reject the kidney?

alexisleigh96 said:

Transplant operations have become routine. One common transplant operation is for kidneys. The most dangerous aspect of the procedure is the possibility that the body may reject the new organ. There are several new drugs available for such circumstances and the earlier the drug is administered, the higher the probability of averting rejection. The New England Journal of Medicine 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. In fact, 20% of positive tests (kidneys are being rejected) and 8% of negative tests (kidneys are NOT being rejected) prove to be incorrect. Physicians know that in about 33% of kidney transplants the body tries to reject the organ. If the new test has a positive result (indicating early warning of rejection), what is the probability that the body is attempting to reject the kidney?

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