| str8outavannuys |
05-23-2005 10:10 PM |
Who likes Math?
Quote:
Originally posted by ThurgreedMarshall
I never took a math course that covered probability. Or, if I did, I was doing something more fun that day.
I was watching Numbers on Tivo the other day and the little professor guy explained a concept in probability using the following example:
Say there are three doors. Behind two doors there is a goat. Behind one door is a new car. What is the probability that you pick the door that has the car? You have a one-in-three chance.
Okay, so you pick the second door. The third door is opened, revealing a goat. Now you have a one in two chance of finding the car.
Here's where it gets tricky. Will your chances of finding the car increase if you change your choice from door two to door one?
I, and all the other dumbass students in his classroom on his show said that it wouldn't. He said we were all mistaken, of course. If you change your choice, apparently you double (or increase, but I think he said "double") the probability that you will find the car.
It doesn't make sense to me because I think the decision to not change doors is as much a choice as deciding to change doors at this point. And I can't get past the fact that no matter which door you choose, when it comes down to two doors, you would have a 50/50 chance of picking the right door.
Someone explain this to me.
TM
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I am 100% sure that someone's beating me to the punch here, but if (as in the "Lets Make A Deal" situation) you have an omniscient Monte Hall-type person choosing to knowingly reveal a goat behind the opened door, which such person will do every time, then if you look at it on an ex-ante basis, by switching your choice, you're increasing your odds from 1/3 (the set of doors your originally chose) to 2/3 (the set of doors you did not originally choose).
Some people find it easier to grasp if you expand the problem to 100 doors, and let's say you choose door #1. And Monte Hall chooses to reveal that every door except door #74 has a goat behind it. Do you want to stick with your original (1-in-100) chance, or do you want to switch? By switching, you "buy" the set of all other 99 doors. It's the same logic in the three-door game.
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