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?

- Pulsified333

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- Pulsified333

@satellite73 @dan815

- anonymous

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

- Pulsified333

okay let me see

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## More answers

- anonymous

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

- anonymous

lets say 10,000 people have the transplant
how many try to reject the kidney?

- Pulsified333

3200

- anonymous

and how many don't ?

- Pulsified333

6800

- anonymous

20% of negative tests prove to be incorrect.
how many is that?

- Pulsified333

of 10000?

- anonymous

no

- anonymous

20% of negative tests are incorrect
that means out of the 3200 people who DO reject, the test is negative and wrong

- Pulsified333

oh

- Pulsified333

so thats not the answer?

- anonymous

what is 20% of 3200?

- Pulsified333

640

- Pulsified333

3200-640= 2560?

- anonymous

those are the people who have a negative nest that is right

- anonymous

now for the next part

- Pulsified333

so is what I did wrong?

- anonymous

wait i think i might have done something wrong, the posiive negative business is confusing
lets back up a sec

- anonymous

6800 do not reject
3200 do reject

- anonymous

out of the the 3200 who do reject, 640 get the wrong answer (negative) and 2560 get the right answer

- Pulsified333

so I have the answer in the work I did earlier

- anonymous

no not yet, and i still got myself confused, damn
we need to work the the 6% now

- anonymous

ok we are good
of the 6800 who do not reject 6% get the wrong answer (positive) so 408 get a positive

- anonymous

now we can finish (thank god)

- anonymous

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

- anonymous

the number that test positive (if i did it correctly) is 2560+408

- Pulsified333

3608

- anonymous

and the number of people who test positive and have it is 2560

- Pulsified333

okay

- anonymous

now we can try this using bayes formula and not numbers if you like
just working with the percents as decimals

- Pulsified333

Pr(A|B) = (Pr(B|A)Pr(A))/Pr(B)

- anonymous

we need the percent of people that you test positive and have it, which is \[.32\times .80\]

- anonymous

that is your numerator

- anonymous

and you need percent who test positive \[.32\times .80+.68\times .06\]

- anonymous

should be the same answer

- Pulsified333

as?

- anonymous

http://www.wolframalpha.com/input/?i=2560%2F%282560%2B408%29

- Pulsified333

Which one?

- anonymous

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

- anonymous

they are the same

- Pulsified333

I see

- Pulsified333

:D it worked thanks.

- Pulsified333

I have to finish as fast as I can so that I can study for my midterm tomorrow

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