We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
"We have a test for a rare disease (we’ll call it Jones Syndrome), and the test is 99% accurate, but it returns a false positive in 1% of those tested (that is, 1% of the time the test returns a positive, the disease is not present). If I test positive, what is the probability that I have Jones Syndrome?"
It's not a trick question, it's a question of simple logic - and that's why it's so easy to fool juries with this sort of thing.
OK, we'll add this data:
"How prevalent is Jones Syndrome, that is, what is the probability of my having it, irrespective of any test result? We’ll say that 1 in 10000 have Jones Syndrome, so your untested probability of having Jones Syndrome is 0.01%, or 0.0001."
I know, I know... "ALBATROSS"!!!! Did I get it right?
You know, you could just have easily copied the full question, including the vital part:
"How prevalent is Jones Syndrome, that is, what is the probability of my having it, irrespective of any test result? We’ll say that 1 in 10000 have Jones Syndrome, so the probability of having Jones Syndrome is 0.01%, or 0.0001."
There I was spending 45 extra seconds (granted far less time than it takes to post this note, but wth) constipating on "wait a minute, did I read this right?", thrown off by the "It's not a trick question, it's a question of simple logic". Bet you're all full and satisfied with yourself. How clever you are. But of course, your purpose (and to some extent, the original author's) was to make a self-satisfying point. Actually, you had no quiz for us at all, since the answer as posted was undefined. Ruddy bastards.
Maybe I think 83% of people who pose misleading questions like this are annoying assholes. Upon later reflection, I find that I was wrong (e.g. false positive) 17% of the time. What are the odds that you are an annoying asshole? There, answer me that...it's not a trick question....
"e.g" means an example follows and "i.e." means a clarification: e.g., I use at is to explain myslef, i.e. to use better words than I did the first time.
There's some high-falutin' Latin for each of them, but hey, the Romans are dead now.
Uh, the "chance" of a person with a true positive having the disease is 100%. If they didn't have the disease they could not have a TRUE positive. I am missing the difference between your two questions.
I kinda thought that was it and I find myself agreeing with you. A swat down could follow any moment from someone who understands stats better than I do.
BTW, annoying a*holes are how we get irritable bowel syndrome.
What an exercise. I read this knowing I could not get the answer as I am not good at this kind of thing, but I gave it a try. In less than thirty seconds Homer's remark flashed across my mind, and I instantly dismissed it knowing I had to be wrong. Then I moved on to the next post. I did eliminate the gratuitous garbage but still did not trust my smarter-than-I intuition.
I once talked with a guy who hired out to large companies to troubleshoot their computer systems. Arduous work at times, but he was so successful that he could not keep up with the demand for his services. I asked him about sequential thinking and the kind of logic required for the work, and he said this: "Don't tell anyone, but it's mostly intuition."