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Forum: General Stuff Topic: Monty Hall Problem started by: thibodeaux Posted by thibodeaux on Jul. 20 2013,05:04
< http://en.wikipedia.org/wiki/Monty_Hall_problem >We've probably talked about this before, but I actually sat down and did it with my kids (with cups and a penny). And I realized there's an extremely simple way to explain how it works. You have a 1 in 3 chance of guessing right. So if you were just playing "guess which door" you'd get it right 33% of the time. We actually did it this way first: I'd hide a penny, and they'd guess. Then I switched to Monty Hall, but I forced them to always switch their choice. And I realized: you only lose if you actually originally guessed the right one. I.e., you only LOSE 33% of the time. Posted by Malcolm on Jul. 20 2013,09:55
Complements. Like statistical, man. I used roughly the same reasoning trying to explain this to non-math folk. If they're going to get it, they usually get it at the point where I say, "Monty always knows which door has the best prize, so ... " However, I also know fully grown adults that still refuse to accept that line of reasoning and go with 50%. Posted by thibodeaux on Jul. 20 2013,10:54
I've always accepted the Bayesian explanation, but I don't truly "feel" it, if you know what I mean.This, I get. Posted by Paul on Jul. 22 2013,06:30
QUOTE Contestants who switch have a 2/3 chance of winning the car, while contestants who stick have only a 1/3 chance. I can't wrap my head around that for some reason. Maybe that's why I suck at math. Let's say they were boxes with a picture of your prize inside. You pick one and he hands you that box, so there are two left: 1/3 of the time you pick the correct box, and Monty Hall will open either of the remaining boxes. 1/3 of the time you pick the wrong box and Monty Hall must open the box on the left. 1/3 of the time you pick the wrong box and Monty Hall must open the box on the right. Since 100% of the time you are left with the unopened box in your hand, one other unopened box on stage, and one opened box with a picture of a goat, I just don't see the advantage of switching. Posted by Paul on Jul. 22 2013,06:40
Okay, I see it now.Since 2/3 of the time he's forced to choose one specific box, 2/3 of the time the remaining box is the winning box. Weird. Posted by thibodeaux on Jul. 22 2013,06:49
I really recommend playing it with your kid. You'll see right away that if you always switch, you will only lose if you actually guessed it right.
Posted by Paul on Jul. 22 2013,06:55
I tried posting this afterward but the page times out:Okay, I see it now. Since 2/3 of the time he's forced to choose one specific box, 2/3 of the time the remaining box is the winning box. Weird. Posted by Malcolm on Jul. 22 2013,07:24
Monty always knows which door has the car and he always opens a door to show a goat."You know, just to be a dick." |