Proving The Monty Hall Problem

This is a method to prove to yourself the results of the Monty Hall Problem. There is something very difficult in trying to describe why you get the result you do. Doing something physical like this can help foster understanding.

Category:

Howto & Style

Tags:

• Proving
• Monty
• Hall
• Problem
• Cards
• Probability
• Understanding

[Solsane]

Another way to view the problem is that your chances of picking correctly with your initial guess (1/3) are unchanged by Monty's revelation. Thus, after one goat is revealed, the chance that the "switch" is correct must be 2/3.

[kirkbocek]

@Solsane Nice. I like it.

[paddygilbert]

It's quite simple to explain.

There are 3 doors, 2 incorrect (goats), 1 correct (car!). You choose one of them. One of the incorrect doors is revealed to be incorrect. You can then switch if you want to. Switching will only work if at first you chose one of the wrong doors. Seeing there are 2/3 wrong doors at the beginning, switching will work 2/3 of the time.

[kirkbocek]

@paddygilbert, I didn't make this for you, you get it. You need to hook up with one of these knuckleheads who swear the answer is 50/50. *Then* you'll see why I made it.

[Sonarghosts]

i dont understand why you went through such extremities to explain this problem. You could just keep the 3 cards face up like the later part and show what would happen if you switched or stayed starting from the first to the last card. To even do any kind of random generation I think kind of confuses than shows any kind of proof. I can flip a coin 100 times and show mixed results or just show that a coin can only fall 2 ways 100% of the time making the probability of landing on a side 50%

[kirkbocek]

@Sonarghosts take a look at my reply to paddygilbert

[JohnnieNaked]

Ok but this is assuming the host knows where the cars and goats are and will always pick a goat to show you. If he doesn't know then it's 33% no matter what you do.

[PeaceLemony]

thanks ;D

[danjor92]

Thumbs up if you thought it was cool that this video was 3:33 before you even watched it;) (33.3333333. . . %)

[R2Mintus]

Part2, it's not 50/50, and 66.6% represent the car b/c a goat was shown. E.g:

Event A) Picked car and stayed = 33.3% of picking car

Event B) Picked car and switched = 33.3% of picking car

Event C) Picked goat and stayed = still 33.3% of picking car

Event D) Picked goat and switched = still 33.3% of picking car plus the 33.3% of the shown goat resulting in 66.6% of picking car if you switched (if you stayed, you're back to 33.3% and NOT 50% because door1=33.3%, dr2=33.3%, dr3=33.3%).

[R2Mintus]

Part1

It's easier to understand if looked from the car perspective (the prize u want):

1) picking a car = 33.3% (one door)

2) picking a goat = 66.6% (two doors)

If you stick to your 1st choice, your best is 33.3%,

but by switching you're trading your 33.3% for the remainder--the 66.6% (in effect, you are choosing TWO doors vs. one door).

So, staying = choosing one door = 33.3%.

switching = choosing two doors (opened door and switched door) = 66.6%.

Basically, opening two doors is better.

[pmelendezu]

Sorry for trolling your video (I am convinced of the switch will win with a 66 % chance btw) but what a terrible random generator (shuffle) you are using that the Ace is always the third card :P

[Reckful222]

Not going to lie very well explained :)

[ValmisFilm]

U know U can even blame the weather for that.