Replies to post #129024 on Biotech Values

[TastyTheElf]

Note: I am interested in how you reconcile having two mutually incompatible answers?

That's easy -- the first was based on the common-sense notion that I would have been tested for the disease based on a strong suspicion that I had the disease, invalidating any notion that there was only a 1% chance I had it.

The second answer presumed that, somehow, I had been subjected to a population-wide test for the disease -- for a disease with a 1% probability, it would be ludicrous to have a test with a 30% false positive rate. That's why I didn't propose this as the only answer. It was the one you were looking for, but the example was based on very odd presumptions. Why would anyone administer a test with a false positive rate of 30% where they pre-determined your odds of having a disease at 1%? Your referencing of the 1% general incidence could simply have been a red herring. You could just have easily then come back and said, "Why would you assume that the test had been given to the whole population? The 1% general incidence stat has nothing to do with the quality of the test when it's performed on someone suspected to have the disease."

It's easy to "trap" someone if you act as if the puzzle is explicit when it isn't. I remember lots of discussions awhile back about that "Let's Make a Deal" puzzle where the host shows you a donkey behind the door after you pick a door, and then you can switch.

It is absolutely critical to that puzzle whether the host knows what's behind the doors in advance. If you assume he does, and that he is tasked to reveal a donkey from the two unpicked doors, then you should always switch. If he doesn't know, and randomly picked a door, and a donkey came up, then there is no point in switching -- the odds are still even for both doors.

I find it ironic that you posited a puzzle meant to instruct one to take everything into account, and then you're surprised when the answer is more complicated because I've taken everything into account.