[kucheravka]

I had a hard time but finally I got it after reading this part

Suppose you're on a game show and you're given the choice of three doors [and will win what is behind the chosen door]. Behind one door is a car; behind the others, goats [unwanted booby prizes]. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one [uniformly] at random. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice? What happens is if your initial selection is a door with goat (say door 1) then the host must show the goat in the remaining doors (2 and 3) and the other door has to have the car, so if you switch you will get the car.

This won't work if you initial selection was the car, because the two remaining doors are goats and the host can open either door.

But the initial chance of geting a goat from the first selection is 2/3, so the probability of getting a car is higher if you always switch.

[KixdricyArrip]

http://en.wikipedia.org/wiki/Monty_Hall_problem

I am trying to figure out how you have a better advantage if you switch.

Here's my thinking, you pick door 1, then host opens up door 3 revealing a goat.

Which means that for the 2 remaining doors you have a 50/50 chance of picking a car.


I fail to see with having 2 remaining doors that you can have a greater than 1/2 chance of guessing correct.

[uchetrip]

The simplest why I have found to explain it to people who don't study conditional probabilities is this (it's pretty much a description of a probability tree):

1) You make an initial choice of 1 in 3, each with equal probability.
2) You are then shown that one of the doors has nothing behind it.
3) The car is now behind one door, giving you a 50/50 chance selection of change or stick, but you already made a 1 in 3 decision, so if you stick with either door you have a 1 in 6 chance, or a total probability of 1 in 3 of winning the car (two lots of 1 in 6 for each door taking all of the remaining initial choices into account)
4) Your change winning probability is therefore 1 - 1/3 = 2 in 3.

People often think you can discount all of the external probabilities that don't affect you, but you can't.

[nizcreare]

So is this one of those probability proofs that technically can be made to seem weirder than it actually is?

I fully understand probability trees and how you multiply down the branches and what have you, but that doesn't take away from the fact that at the 2nd decision, there is a 50/50 chance it's behind either door.

[uchetrip]

So is this one of those probability proofs that technically can be made to seem weirder than it actually is?

I fully understand probability trees and how you multiply down the branches and what have you, but that doesn't take away from the fact that at the 2nd decision, there is a 50/50 chance it's behind either door.

But you made a 1 in 3 to get to 50/50. You could have made a 1 in 3 and won the car, but you didn't, so you're now being offered a 50/50 that had 2 in 3 ways of being offered. You have been provided with more information than a straight 50/50 choice.

[nizcreare]

So at the 2nd choice the branches would be 2/3 x 1/2 (success) or 2/3 x 1/2 (failure)

If you reach the 2nd choice, either way it's a 1/3 that you'll get the car or goat.

The prior failure to pick the car at the first pick has no bearing on which door to pick second time around.

[uchetrip]

I'll jut post the diagram that was even on the first link:

http://upload.wikimedia.org/wikipedi...tree_door1.svg

EDIT: this doesn't exactly cover what I was explainging as I was describing car, nothing, nothing rather than car, goat, nothing but the principle is the same.