Monty Hall Problem

Post by **thibodeaux** » Sat Jul 20, 2013 8:04 am

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.

Malcolm · Post by **Malcolm** » Sat Jul 20, 2013 12:55 pm

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%.

Post by **thibodeaux** » Sat Jul 20, 2013 1:54 pm

I've always accepted the Bayesian explanation, but I don't truly "feel" it, if you know what I mean.

This, I get.

Paul · Post by **Paul** » Mon Jul 22, 2013 9:30 am

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.

Paul · Post by **Paul** » Mon Jul 22, 2013 9:40 am

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.

Post by **thibodeaux** » Mon Jul 22, 2013 9:49 am

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.

Paul · Post by **Paul** » Mon Jul 22, 2013 9:55 am

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.

Malcolm · Post by **Malcolm** » Mon Jul 22, 2013 10:24 am

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."

Edited By Malcolm on 1374503275