Quote:2) In the original game, I think Monty Hall might have opened one of the doors at random. If he opened the door with the good prize, I think you could just switch to that one and win 100% of the time.
Maybe, the first time it was played. But when I watched Let's Make A Deal back in the 70's, it was always always always a "bad" door that was opened up before the choice of switching was made.
I don't think this door switch game, tho, is the best example to illustrate Bayes Theorem, at least not for the way I learned Bayes.
IIRC the best examples are the ones using medical tests -- ... hmmm, say the odds of you (as an untested person) having Gödel's Syndrome are 1 in 10,000, the odds of getting a false positive are .01 and the odds of getting a false negative is .005, and you get a "positive" test result, what is the (new) probability that you actually have the disease??
Hmm, test 10000 people, get 99.99 false positives, and 0.995 real positives. So the odds of you actually the disease are (0.995)/(99.99+0.995) or 0.009853. (That's the Bayes part, the division.
So, even though the test is 99% accurate, your actual odds of having the disease are still less than one percent. Sure, that's much higher than 1/10000, but it's not anything near 99/100.
-V
edit: added quote to quote