#### RE: The Doctor, and the rare disease...

Right this is a long thread, so this hopefully won't get read....

There is this disease, that affects all people in equal proportion at a rate of 1 in 100 000. Assuming your a normalish human being, your chances of getting the disease is 1/100 000.

Now you go to the doctor for a routine check up (ie. the disease doesn't present any symptoms except sudden death) where he does a battery of tests. Guess what, the test comes back positive for sudden death disease.

"Lucky" for you, there is a cure, that is 100% effective, but which kills you if you don't have the disease. The doctor then tells you the test for the disease is 90% accurate. That is, if it says you don't have it, there is a 10% chance that you actually do, and if it says you don't, there is a 10% chance that actually you do.

Thus, the question is, what is the probability that you have the disease, given that the test was positive?

Applying Bayes' Theorem, hopefully correctly, gives:

(0.90*0.000 01)/(.9*0.000 01 + 0.1*0.999 9)

= 9 in 111 119 or roughly 0.0081%

or roughly 1 in 10 000.

So, no, don't take the "cure", except if your feeling really unlucky, who knows, you could be the 1 in 100 000 person who actually has the disease.

http://en.wikipedia.org/wiki/Bayes'_theorem