## Pulsified333 one year ago 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?

1. Pulsified333

@satellite73 @dan815

2. anonymous

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

3. Pulsified333

okay let me see

4. 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

5. anonymous

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

6. Pulsified333

3200

7. anonymous

and how many don't ?

8. Pulsified333

6800

9. anonymous

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

10. Pulsified333

of 10000?

11. anonymous

no

12. anonymous

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

13. Pulsified333

oh

14. Pulsified333

15. anonymous

what is 20% of 3200?

16. Pulsified333

640

17. Pulsified333

3200-640= 2560?

18. anonymous

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

19. anonymous

now for the next part

20. Pulsified333

so is what I did wrong?

21. anonymous

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

22. anonymous

6800 do not reject 3200 do reject

23. anonymous

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

24. Pulsified333

so I have the answer in the work I did earlier

25. anonymous

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

26. anonymous

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

27. anonymous

now we can finish (thank god)

28. 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

29. anonymous

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

30. Pulsified333

3608

31. anonymous

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

32. Pulsified333

okay

33. anonymous

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

34. Pulsified333

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

35. anonymous

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

36. anonymous

37. anonymous

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

38. anonymous

39. Pulsified333

as?

40. anonymous
41. Pulsified333

Which one?

42. 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

43. anonymous

they are the same

44. Pulsified333

I see

45. Pulsified333

:D it worked thanks.

46. Pulsified333

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