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 re(4): solution by Penny)

Sounds like a good idea, but then how many times would we have to run the governor's race in the state of Washington? 

But then, an election isn't really analogous to one test with a small chance of type I and type II errors.  It's more like each person voting is one test with a small chance of the person making a voting error, such as a hanging chad, or significant voter fraud.  So an election where 100 million votes are cast is more like the test was run 100 million times.  And since over 3 million more votes for one candidate than the other the outcome is clear.

Posted by Larry on 2005-01-03 22:39:13