Transplant operations have become routine. One common transplant operation is fo

Question

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 negative tests and 8% of positive tests prove to be incorrect. Physicians know that in about 31% 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? please explain your answer, Thank you :)

Explanation / Answer

P(body attempting to reject) = 0.31

P(body not attempting to reject) = 1-0.31 = 0.69

P(body is attempting to reject kidney | positive test result) = P(body is attempting to reject kidney and test result is positive)/P(positive test result)

= P(body is rejecting and positive)/[ P(body is rejecting and positive) + P(body is not rejecting and positive) ]

= 0.31x(1-0.08) / (0.31x0.92 + 0.69x0.20)

= 0.2852/0.4232

= 0.6739

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