Question

Game show gambit: A participant in a game show is offered a choice of one of three boxes, only one of which contains a prize. After the participant chooses a box, the emcee opens one of the other two boxes and shows that it is empty. Then the emcee asks: "Do you want to stick with your choice, or would you rather pick the other box?" Naturally one wants to maximize the odds, but will switching do it? What would you do? Make your decision - and justify your answer!

Answer 1

goat and car

Answer 2

always switch. Because the probability that it will be in the switched one is 2/3 as opposed to the one you originally chose which is 1/3

Answer 3

I don;t know that one, I'll have to look for it!

@Luminaire, yes, but why are the odds twice as high if you switch?

Answer 4

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

Answer 5

Think about it like this: Boxes A. B , C
you chose A.
There is a 1/3 probability that you are right. (and you should stay on it)
If it was actually in B, he will open C for you, ( and you should switch to get the right one)
if it was in C, he will open B, (so you should switch to get the right one)
Therefore probability of switch to get right answer is 2/3
probability of not switch for right answer is 1/3

Answer 6

@ Luminaire
You are correct but I'm not clear on you logic.
I would state this as such:
You initially had a 1/3 chance of being correct and a 2/3 chance of being wrong. Removing one box means you still have a 1/3 chance that you were correct initially. Since the odds are that 2/3 that you chose the wrong box initially, the other box now has odds of 2/3 of being the correct one.

Answer 7

@Tomas
I had no idea the history of this problem and its relation to monty python. That article is hilarious, thanks!

Answer 8

Yes, that is right. I wrote it another way to emphasize that if there were 100 boxes, it would be really obvious

Answer 9

True, that would make it more clear, but as Tomas' link shows, even PhD mathematicians contested the idea initially :)

Answer 10

Wanna try my other one?
http://openstudy.com/#/updates/4ede85b2e4b05ed8401aa2f6

Answer 11

I just posted link to wiki so you could read there, because it's explained very good

first time I met this idea was in movie called 21, it's good movie, you should watch it :P