Does This Make Sense To You?
Remember the old Monte Hall show where you could choose your prize behind one of three doors? Say there was a Caribbean cruise behind one. Behind the other two were a can of sardines or a goat or something. So you'd choose your door, then Monte would open one of the other doors showing a dud gift and give you a chance to switch your original choice with the last unopened door.
You with me so far?
Should you switch doors, or stick with your original choice? Does it make a difference? Common intuition tells us we have a 50/50 chance with the remaining doors, so it doesn't make a difference, right? But this article claims that mathematically you should switch.
Why? Because in this scenario your original choice would only be right 1 out of 3 times. If you switch you are betting on it being wrong, which happens 2 out of 3 times.
Yet, I'm not convinced. What's the difference between letting Monte open one of the dud doors and *then* choosing? Does it somehow magically affect the odds that we've chosen before rather than after? If after, then the case is clearly 50/50. What makes us think that the switching of doors is not the *wrong* answer, thus part of the 2 out of 3? Or what about just thinking of our first choice and then betting against ourselves by choosing one of the other two.
I'm not sure though, the mind has a weird tendency, especially when dealing with probability, to get things dead wrong. It's something to think about the next time you're in a waiting room somewhere with nothing to do :-)
You with me so far?
Should you switch doors, or stick with your original choice? Does it make a difference? Common intuition tells us we have a 50/50 chance with the remaining doors, so it doesn't make a difference, right? But this article claims that mathematically you should switch.
Why? Because in this scenario your original choice would only be right 1 out of 3 times. If you switch you are betting on it being wrong, which happens 2 out of 3 times.
Yet, I'm not convinced. What's the difference between letting Monte open one of the dud doors and *then* choosing? Does it somehow magically affect the odds that we've chosen before rather than after? If after, then the case is clearly 50/50. What makes us think that the switching of doors is not the *wrong* answer, thus part of the 2 out of 3? Or what about just thinking of our first choice and then betting against ourselves by choosing one of the other two.
I'm not sure though, the mind has a weird tendency, especially when dealing with probability, to get things dead wrong. It's something to think about the next time you're in a waiting room somewhere with nothing to do :-)
Boy, I got dizzy just trying to figure this out, lol
ReplyDeleteAfter thinking some more about this, I think the math geeks are right. You should always switch.
ReplyDeleteLet's say you picked door #1 and it was the prize but you switched. Given that you will be right only 1 out of 3, you'd get the dud prize 1 of 3 times by switching... but
If door #1 was the dud and you switched, you'd be right 2 out 3.
So if you always stuck with your first choice, your odds are 1 in 3. If you always switched, you're betting on the 2 out of 3 odds.
Of course, this assumes intuition plays no role. A big assumption.