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 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?

Answer 1

@satellite73 @dan815

Answer 2

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

Answer 3

okay let me see

Answer 4

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

Answer 5

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

Answer 6

3200

Answer 7

and how many don't ?

Answer 8

6800

Answer 9

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

Answer 10

of 10000?

Answer 11

no

Answer 12

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

Answer 13

oh

Answer 14

so thats not the answer?

Answer 15

what is 20% of 3200?

Answer 16

640

Answer 17

3200-640= 2560?

Answer 18

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

Answer 19

now for the next part

Answer 20

so is what I did wrong?

Answer 21

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

Answer 22

6800 do not reject
3200 do reject

Answer 23

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

Answer 24

so I have the answer in the work I did earlier

Answer 25

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

Answer 26

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

Answer 27

now we can finish (thank god)

Answer 28

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

Answer 29

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

Answer 30

3608

Answer 31

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

Answer 32

okay

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

that is your numerator

Answer 37

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

Answer 38

should be the same answer

Answer 39

as?

Answer 40

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

Answer 41

Which one?

Answer 42

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

Answer 43

they are the same

Answer 44

I see

Answer 45

:D it worked thanks.

Answer 46

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