A very simple probability question...

[nile455]

Say you're participating in a contest where the host lets you choose from one of three closed boxes. You are told that one of the boxes contains $10,000 dollars, but the other two are empty. If you pick the one with the $10,000 you get to keep it. The host of the contest knows which box has the prize.

You tell the host your selection and then he opens up one of the two boxes you didn't pick, and it's empty. There are two boxes left, one of them contains the prize. The host then decides to give you the option of changing your original selection.

What should you do? Change your selection? Or should you stick with your first instinct? Or does it not matter?

 

[minkydog]

I would not. As I see it I'd have a 50:50 chance of finding the $10,000. And if I got nothing, well I got there with nothing

 

[mickeymedic]

Well, once you're down to 2 boxes you have a 1 in 2 chance of picking the right box no matter which box you pick. I would not change my choice. I have always been taught to go with my first instinct.

 

[BCDisneyFanatic]

Say you're participating in a contest where the host lets you choose from one of three closed boxes. You are told that one of the boxes contains $10,000 dollars, but the other two are empty. If you pick the one with the $10,000 you get to keep it. The host of the contest knows which box has the prize.

You make your selection, and then the host opens up one of the two boxes you didn't pick, and it's empty. There are two boxes left, one of them contains the prize. The host then decides to give you the option of changing your original selection.

What should you do? Change your selection? Or should you stick with your first instinct? Or does it not matter?

You switch.

There is 2 in 3 probability that the one of the other two boxes will contain the money. Since the host knows which one contains the money, and will only show the box without it, there is a greater chance that the money will be in the remaining box than in the one you originally chose.

 

[Bluestars]

I read somewhere, although I can't remember where, that you should keep your original choice. Something about once a box is revealed to not contain the prize, the odds go up that you have selected the box with the prize.

ETA, after reading the above post, I probably have it reversed.

 

[Acklander]

I'd change. I'd go with the logic of the first time I picked I had a 1 in 3 chance of being right, and the second time I picked of a 1 in 2 chance of being right, so by swapping that should up my odds.

 

[BCDisneyFanatic]

To explain further:

There are three possibilities: The money is either in Box A, B or C.

If the money is in Box A and you chose Box A, then the host will show either box B or C...doesn't matter. If you keep it, you win; if you switch, you lose.

If the money is in Box B and you chose Box A, then the host will open Box C. The other unopened box contains the money. If you kept your box, you lose; if you switch, you win.

If the money is in Box C and you chose Box A, then the host will open Box B. Once again, the other unopened box contains the money. If you kept your box you lose; if you switch, you win.

Two out of three times you'd win by switching boxes.

 

[nile455]

Yes, the correct answer is to SWITCH.

 

[LadyZolt]

This is known as the "Let's Make a Deal" problem or the "Monty Hall" problem because Monty Hall on that TV show did know where the prize was and would often allow people to switch after he opened or revealed one door or curtain that wasn't the "good" prize. You should switch, as Marilyn vos Savant said in "Parade" magazine a while back. Here's an article:

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

And here's a site that explains it and has a simulation you can play yourself if you don't believe. Play it a dozen times and see how often switching wins compared to not switching. Click on "Three Doors Simulation" after scrolling down to the "links to websites" area:

http://www.letsmakeadeal.com/problem.htm

 

[MiniGirl]

Yes. You switch.

It is also used in a classroom scene in the movie "21."

 

[Katie's Butterflies]

To explain further:

There are three possibilities: The money is either in Box A, B or C.

If the money is in Box A and you chose Box A, then the host will show either box B or C...doesn't matter. If you keep it, you win; if you switch, you lose.

If the money is in Box B and you chose Box A, then the host will open Box C. The other unopened box contains the money. If you kept your box, you lose; if you switch, you win.

If the money is in Box C and you chose Box A, then the host will open Box B. Once again, the other unopened box contains the money. If you kept your box you lose; if you switch, you win.

Two out of three times you'd win by switching boxes.

Wow that’s interesting. I would have thought it wouldn’t matter, but what you said made sense.

And here's a site that explains it and has a simulation you can play yourself if you don't believe. Play it a dozen times and see how often switching wins compared to not switching. Click on "Three Doors Simulation" after scrolling down to the "links to websites" area:

http://www.letsmakeadeal.com/problem.htm

Though when I tried this game, I picked the correct door each time, so for me it wouldn’t be a good idea to switch.

 

[Carly_Roach]

The only way to win is to not play the game.

If my host wants to give me $10,000 then he should just give me the money.

 

[nile455]

This is known as the "Let's Make a Deal" problem or the "Monty Hall" problem because Monty Hall on that TV show did know where the prize was and would often allow people to switch after he opened or revealed one door or curtain that wasn't the "good" prize. You should switch, as Marilyn vos Savant said in "Parade" magazine a while back. Here's an article:

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

And here's a site that explains it and has a simulation you can play yourself if you don't believe. Play it a dozen times and see how often switching wins compared to not switching. Click on "Three Doors Simulation" after scrolling down to the "links to websites" area:

http://www.letsmakeadeal.com/problem.htm

Yep, thanks for the link. I purposely avoided referring to the Let's Make A Deal show because I didn't want anyone being able to google the answer at first.

It's a fascinating paradox.