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 6% of positive tests prove to be incorrect. Physicians know that in about 32% 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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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 6% of positive tests prove to be incorrect. Physicians know that in about 32% 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?

Mathematics
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kind of wordy isn't it? probably a bayes formula question lets see if we can cut through the verbiage
okay let me see

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Other answers:

this stuff is usually confusing as hell one way to break through the confusion is to forget about probability and percents, and work with nice large whole numbers to see what is going on
lets say 10,000 people have the transplant how many try to reject the kidney?
3200
and how many don't ?
6800
20% of negative tests prove to be incorrect. how many is that?
of 10000?
no
20% of negative tests are incorrect that means out of the 3200 people who DO reject, the test is negative and wrong
oh
so thats not the answer?
what is 20% of 3200?
640
3200-640= 2560?
those are the people who have a negative nest that is right
now for the next part
so is what I did wrong?
wait i think i might have done something wrong, the posiive negative business is confusing lets back up a sec
6800 do not reject 3200 do reject
out of the the 3200 who do reject, 640 get the wrong answer (negative) and 2560 get the right answer
so I have the answer in the work I did earlier
no not yet, and i still got myself confused, damn we need to work the the 6% now
ok we are good of the 6800 who do not reject 6% get the wrong answer (positive) so 408 get a positive
now we can finish (thank god)
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? it is the number of people who do reject and test positive, divided by all that test positive
the number that test positive (if i did it correctly) is 2560+408
3608
and the number of people who test positive and have it is 2560
okay
now we can try this using bayes formula and not numbers if you like just working with the percents as decimals
Pr(A|B) = (Pr(B|A)Pr(A))/Pr(B)
we need the percent of people that you test positive and have it, which is \[.32\times .80\]
that is your numerator
and you need percent who test positive \[.32\times .80+.68\times .06\]
should be the same answer
as?
http://www.wolframalpha.com/input/?i=2560%2F%282560%2B408%29
Which one?
i made a typo in the first one http://www.wolframalpha.com/input/?i=%28.32*.80%29%2F%28.32*.80%2B.06*.68%29
they are the same
I see
:D it worked thanks.
I have to finish as fast as I can so that I can study for my midterm tomorrow

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