Should You Switch Doors?

[slonezp]

Pulled this off another forum. What are your opinions?

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 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 switch your choice?

[Raider Nation Fisher]

Nope. Stick with your first choice.

[preach4bass]

Statistically speaking, you should switch doors. You have a 33.3% chance of picking the right door with your first guess. That leaves you with a 66.6% chance that your first guess is wrong. Eliminating one of the wrong choices dosn't change your initial chances. So, statistically, if you switch doors, you would then have a 66.6% chance of picking the right door and winning a car!

[Raider Nation Fisher]

Hmmmmm. The statistic is 66.6%. So if I remove the . from that figure then the devil will help me out. Heh heh I like them odds.

[The Rooster]

I disagree. After you eliminate one choice, your odds are now 50/50, not 33/66. You have a 50% chance of getting it right if you switch or stay after you know the 3rd choice was wrong.

Now, staying or switching, there is no advantage one way or the other. It's a shot in the dark no matter what.

[Long Mike]

I agree with Rooster. The choice is now 50/50.

[Bassn Blvd]

I disagree. After you eliminate one choice, your odds are now 50/50, not 33/66. You have a 50% chance of getting it right if you switch or stay after you know the 3rd choice was wrong.

Now, staying or switching, there is no advantage one way or the other. It's a shot in the dark no matter what.

^^ X2.^^

If anything, you have an increased chance that your door will have the car behind it after one of the "goat" doors has been eliminated.

[SirSnookalot]

Rooster is right.

[preach4bass]

I'm not a betting man. But, if I were, I wouldn't let you fellas pick my "winners"!

This is an old applied mathmatics problem that was recently used on the show "NUMB3RS".

[moguy1973]

Mythbusters did this test too. If you stick with your original door your chances remain at 1 out of 3 (33.3%). If you switch your door after the host reveals one that increases your chances to 1 out of 2 (50%). They showed it was better to switch doors because there's a better chance that other door has the prize since the host knows the one he opened isn't the prize.

It's confusing but they explain things better here: http://community.discovery.com/eve/forums/a/tpc/f/9401967776/m/74419288901/p/1

[slonezp]

Here's another link

http://farmdev.com/thoughts/41/the-monty-hall-problem-win-a-goat-or-a-car-/