[Guest]

This is an old one I heard a long time ago before deal or no deal:

You are on a game show. The host shows you ten doors. He says one door has 10 million dollars behind it, the other 9 doors has nothing. You must pick a door. So you do.

Now the host says, "Let's see how you did."

He opens a door, nothing.

He opens another door, nothing.

He opens another door, nothing.

He repeats this until there are only 2 doors left unopened: the door you picked and another door.

Now he says, "The prize is behind one of these two doors. You can stay with your door, or switch to the other door."

Should you stay with your door, or switch doors? Why?

What is the probability of winning for each door?

[Guest]

This is an old one I heard a long time ago before deal or no deal:

You are on a game show. The host shows you ten doors. He says one door has 10 million dollars behind it, the other 9 doors has nothing. You must pick a door. So you do.

Now the host says, "Let's see how you did."

He opens a door, nothing.

He opens another door, nothing.

He opens another door, nothing.

He repeats this until there are only 2 doors left unopened: the door you picked and another door.

Now he says, "The prize is behind one of these two doors. You can stay with your door, or switch to the other door."

Should you stay with your door, or switch doors? Why?

What is the probability of winning for each door?

This is the same as monty hall problem. It is better to switch doors. The door you picked has a probability of 1/10 while the other door has 9/10 probability of containing the 10 million dollars

[Guest]

There is an even 50/50 chance of each door. As doors are opened, the odds of each door change. Just because 1 door started out with 1/10 chance of winning does not mean it stays that way. If one of the earlier doors had the money, the rest of the doors chances would change to 0%. If you walked in the middle of the game, and the rules were: There are 10 doors, the first 6 don't have anything behind them, what are the odds of the money being behind one of the last four doors, you would calcualate the odds for each door at 1/4, not 1/10.

[Guest]

There is an even 50/50 chance of each door. As doors are opened, the odds of each door change. Just because 1 door started out with 1/10 chance of winning does not mean it stays that way. If one of the earlier doors had the money, the rest of the doors chances would change to 0%. If you walked in the middle of the game, and the rules were: There are 10 doors, the first 6 don't have anything behind them, what are the odds of the money being behind one of the last four doors, you would calcualate the odds for each door at 1/4, not 1/10.

sorry but you appear to be wrong (I think if I understand you correctly)

each door had 1/10 chance. You choose one randomly, it has 1/10 chance of being the correct door. so 9/10 times you have not picked the correct one. The man then opens 8 other doors (and never chooses the one with the money if it's there), all being empty, and therefore it's either your door (1/10) or it's not your door (9/10). Therefore it's better to switch, you have a 9/10 chance of winning the money if you switch.

I hope that makes sense.

[Guest]

There is an even 50/50 chance of each door. As doors are opened, the odds of each door change. Just because 1 door started out with 1/10 chance of winning does not mean it stays that way. If one of the earlier doors had the money, the rest of the doors chances would change to 0%. If you walked in the middle of the game, and the rules were: There are 10 doors, the first 6 don't have anything behind them, what are the odds of the money being behind one of the last four doors, you would calcualate the odds for each door at 1/4, not 1/10.

What might help here is to think about WHEN the choices are made. the door you choose was chosen at a point giving it a 1 in 10 chance. You have more knowledge at the time you are given the choice to switch. Because the host is picking doors that he knows are empty (the riddle should have pointed this out as it is the key) you now know your door has 1 in 10 and the other has to be 9 in 10 . If someone walks into the room and just sees 2 doors and does not know what has happened, then yes, it would be a 50/50 choice for THEM but not for you.

The hosts choice is the key.

Edited October 2, 2009 by Chewbacca

[rookie1ja]

Welcome to the Den, dontgivemetheanswer. This is one of my favorites and I have even put it on a separate page dedicated to the Best Puzzles. Note that there is also including more than 150 replies.

To keep all important information on 1 place I close this thread and you can continue discussion in the old thread if you have anything substantial to add (which would be a bit hard since there are +150 good replies :-).

Enjoy the Den