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Which door should you choose?

Imagine being in a game show. You have three doors in front of you. The prize, say a reasonable sum of money, is behind one of them but behind the other two there is a custard pie. If you open the door with the prize behind it then this is what you win. If you reveal a custard pie then the custard pie will be thrown in your face. Now you choose a door but you don't yet open it. The game show host reveals opens one of the doors to reveal one of the custard pies. Now you're allowed to change your mind at this point. What do you do and why?

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SealedWithAKisss

Door #2

custardpied · 51-55, M

Okay you have chosen door 2 but you have not opened it. I then open another door with one of the custard pies behind it. Should you change your mind?

SealedWithAKisss

Nope I'm sticking to my guns what did I win?

custardpied · 51-55, M

It's a probability problem but if you stick with your first choice then unfortunately you are twice as likely to receive the custard pie in your face than the prize.

custardpied · 51-55, M

It's called the Monty Hall Problem. Maybe you already understand it but in any case I will post an explanation a bit later. I personally did not find this easy to understand but it is interesting.

custardpied · 51-55, M

Okay here's the explanation. You have three doors with a prize behind one and a custard pie behind the other two. If you choose a door the probability that you have chosen the prize is a third. The probability that you have chosen a pie is two thirds. Now before opening the door I open one of the doors with a pie behind it. Now it is still more likely that you have chosen a pie. If you're given the chance to change your mind then you should. If you stick to your guns you still have a probability of a third of receiving the prize. If you change your mind then the probability of receiving the prize is two thirds. This took me a while to understand. By sticking to your guns you're twice as likely to receive a custard pie in your face! Not pleasant!