What is the probability of choosing a 1 or 2?

Question

a game show host conceals a prize behind 1/3 curtains number 1 2 3. asked to guess where the prize is, you choose 1. before disclosing the prizes location, the host opens 3, revealing that it is not there, and offers you the option of sticking with 1 or switching to 2. what should you do to maximize your chance of winning?

Answer 1

There is 1 major factor here that is usually forgoten. There will always be an empty door to take away. There are 2 empty doors to start with and you only have one to pick. And since you can't pick 2, the other empty door wich is guaranteed to be there, is taken away. So...

The probability of picking it right is 50 / 50. Exactly even.

There is no possible way to maximize an even bet. Whether you switch your choice or not it will still be 50 /50. Switching will not change it to 49 / 51 or 45 / 55. No psycological explaination will change the odds from being exactly even.

By eliminating 1 option, they just changed it from 33.333333% chance of getting it right to 50%.

At the end of thier logic, they say 2 / 3's of the time if you  switch you win. It's not in thirds any more its in half.

If the 3rd empty door isnt even really there to begin with. Theres 2 doors.

Also ask yourself this question. If i switched my choice, then the host offered me even 1 more time to switch, would switching 1 more time increase or decrease my chances of winning. Its the same because theres 2 choices.

The magical 3rd door isn't even there to begin with. LOL

Answer 2

Congrats. You are the one millionth person to ask me about the Monty Hall problem.  It's a question that has caused much debate and argument between statisticians, game show fans, and every other person ever to read the question.  To me it's just an example of how not defining a question well can cause more problems than anything else.

if you want to learn more about his problem you can check this link out:

http://math.rice.edu/~pcmi/mathlinks/mon...

Answer 3

change your choice to number two. I forget who it was, but a well renowned mathematician proved that changing your answer improved your chance of winning

Answer 4

Id change to 2, i saw it in the movie "21" not gonna lie

Answer 5

I've seen this question show up several times since the movie "21" came out.

Wikipedia has had a nice article up for quite a long talking about how the math actually works.

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

It's informative and should help clear things up, includes pictures too!

Answer 6

you only have one shot. and now it would be a 50% chance of winning.

Answer 7

Yes, this is the famous Monty Hall Problem.  You can GOOGLE it and come up with dozens of hits.

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

If (and this is a big IF) the problem stipulates that the host will always reveal a door without a prize (since the host knows ahead of time which door has the prize) then yes you should switch.  You increase your chances of winning from 1/3 to 2/3 if you switch.  (Yes, your odds are now 2/3... NOT 50-50.)

I have to wonder how many unfortunate people who actually appeared on Monty Hall's game show, didn't know this!  Probably a lot, because the answer is counter-intuitive.

Answer 8

To maximize your chance of winning, you need to analyze the host.

Is he evil, and trying to get you to lose?  If so, don't switch, because if you had already chosen poorly, he wouldn't be giving you another chance.

Is he kind, and offering you a shot at redemption?  If so, then you can assume he wouldn't be hurting you, and switching is a good idea.

Is he neutral, and only following the rules of the game, and are the rules the typical 'always open a curtain and give the choice, never reveal the prize' kind?  then swith and double your chances.

And finally, is he confused, and drooling on his shirt as he stares blankly ahead?

In that case, don't switch.  Your odds of winning are 50-50, but the pain of knowing you had already picked the winner and gave it up is far greater than the pain of knowing you had a chance of switching to the winner but didn't.  {of course, if he's that confused, you should grab the prize, give him a big smile and a wet kiss, and run for the exit.  He's obviously too befuddled to notice.