Monty Hall Problem

3.5 stars

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats.

You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat.

He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?"




Yes it's in your interest because the host (Monty) will always choose a door with a goat behind it.  

  • Hard
  • Logic
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I don't see the logic in this. If the host always opens a door revealing a goat then it does not matter whether or not you switch you're effectively left with a 50/50 choice every time. Finding out that there is in fact at least one goat unchosen changes nothing, you knew that already.
- somedudeonline (8 Jul 2013)

Your solution is incorrect.
In the beginning when you choose you have the probability of 1/3 being correct, or in other words, 2/3 of being wrong.

Chances are, you chose the wrong one so when the host takes out one of the doors that is for sure wrong, you can switch your door up and have a better chance of getting the winning door. Basically you are gambling on choosing the wrong door to begin with.
- Mike (31 Aug 2013)

I agree with mike although I see where you thought the 50/50chance was right
- (6 Jan 2014)

At the beginnig, your chance (of choosing the car) is 1/3; but after the goat door is opened its now 2/3. So don't change your door.

Assume there are 100 doors and the host opened 98 goat-doors and asks you to change your door, don't; because your chance is 99/100.
- Archy (10 Jan 2014)

I think you mean DO change your door (assuming you want to win the prize and not a goat) as you have a 2/3 chance of winning (or 99/100 chance with a 100 doors) if you switch doors
- PalmerEldritch (6 Feb 2014)

Archy, that's the 1st time I've ever heard anyone say your chances double if you stick with your 1st pick.
Congratulations on a highly original but (unfortunately) incorrect answer.
- PalmerEldritch (13 Feb 2014)

Anyone ever watch mythbusters? They did an episode on this very idea. U do not want to, psychologically. Jamie never switched, Adam always switched, guess who won?
- Thisisfuntocomment (26 Apr 2014)

Here's another way to look at it. Say you own the show and you randomly put the car behind curtain two. Now run through the scenarios. Contestant picks one, he switches and wins. Contestant picks two, he switches and loses. Contestant picks three, he switches and wins. Two out of three scenarios, the contestant wins when switching. The advantage is gained by the show always having to expose a goat. With no goat exposed, there are four scenarios. Two wins out of four. Squeezing the scenarios down to three is the show's generous gift to contestants and not bad for ratings. 'tis good to own a show.
- Dave (4 Aug 2015)

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