Suppose an illness that can affect 1% of the people. Also assume that there is a test for that illness, that gives the correct result 99% of the times.

If you take that test, and receive a POSITIVE result, should you worry much?

If you take it again, and once more get a POSITIVE, should you worry then?

How many consecutive POSITIVEs would you have to get in order to be sure that the chances of a wrong diagnostic are 1 in a million?

(In reply to Correct Solution. by A)

For the first test:

 

You have 1% chance of having this disease. 99% of the time when you have the disease, the test reveals that you have the disease. The odds of a true positive are therefore 99%*1% = 0.99%

When you don't have the disease (99% of the time), you get tested as a positive (false positive) 1% of the time. The odds of getting this false positive is 1%*99% = 0.99%

Therefore, the odds of having a true positive is .99%/1.88% = 1/2

If you tested positive the first time and take it again, the odds of again receiving a positive if you truly have the disease would be 1%*99%*99% = .9801%

If you tested positive and do not have the disease, however, your odds of a second false positive are 1%*1%*99% = .0099%

Therefore, the odds of truly having the disease after two positive tests is .9801%/.99% = 99%

 

Posted by Marc on 2005-10-19 23:10:44