(March 13, 2016 at 12:20 am)Chas Wrote:(March 8, 2016 at 10:03 pm)Excited Penguin Wrote: You can find me any proof you like, it still doesn't make sense that probability helps you in that scenario. I will say it's all luck since you can't explain it.
As I already said, the fact that the moderator takes out all the bad variants but for one doesn't tell you anything about whether you made the right decision or not. Just the fact that he takes out all the other doors, doesn't mean that he made the unchosen left variant any more plausible than the one you already chose. And that's because no matter if you were wrong or right at first he was going to take out the same number of doors after you made your choice.
In some cases people refer to the 2/3 logic. That's bad logic. It's not 2/3 anymore because there's no three left. There are only two options left and so it's 50/50, not 25/75.
You are admitting, even bragging about, being ignorant.
I suggest you study probability because you really do not understand it.
What is ironic is that when this first appeared in some Sunday newspaper insert a number of math professors wrote in to respond to the columnist precisely as you did EP. However they scolded her because they agreed with EP -incorrectly of course. They suggested she purchase a basic textbook on probability and study it so that she would come to understand that switching would not help, since the probability was 'obviously' 1/2 that either remaining door had the big prize.
The intuition that the odds are 50 to 50 that your original choice was correct (once a wrong choice is revealed) is very powerful. It arises because of a bad analysis resulting from failing to take proper account of the significance of that wrong choice. The probability when the wrong choice is revealed does not alter the probability you had at the outset. I also was flummoxed when I first heard of the problem but also intrigued of course.
A similar problem which probably won't (but might) help is the three domino problem. One has an X on both sides, one has an O on both sides and one has one X and one O on opposite sides. You draw one domino from the bag and hold it facing you and see an X. What is the probability that there is also an X on the other side?
The wrong analysis goes:
There are two dominos I could be holding, the X-X or the X-O.
So the probability that there is an X on the other side is 1/2.
But the correct analysis is:
I could be looking at one of three X's.
There is another X on the back of two of those X's and an O on the back of the third one.
So the probability is 2/3 that there is an X on the other side.
