Let's Make a Deal
Suppose you're on a game show, and you're given a choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number. 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors?
15
comments from:
Melissa,
Michael,
Melissa,
Michael,
Michael,
Melissa,
Melissa,
Michael,
Melissa,
Caci,
Patti,
Melissa,
Michael,
Patti,
Michael,
15 Comments:
Why would I want to switch to a new door. The dude just told me where the goat was!
Two doors have goats behind them, one door has a car. He just showed you where one of the goats is located. There are still two closed doors. Do you want to switch?
Ok, so you totally just missed me "trying" to be funny! Oh, well. I am however still trying to figure out the answer to this question.
Ahhh...I was wondering if they taught you how to count at Byrd. Anyway, if you can't figure it out let me know. This is a Magnet level puzzle after all. DOH!
And those of us that are under the age of 40 know that I was using the term popularized by Homer Simpson. DOH!!
I'm guessing that right about now, Michael is getting frustrated with the fact that no one has attempted to answer the question. Am I right, Michael?
Ok, so I pick door number 1 and he opens door number 3. There is a goat behind door number three. I still don't know what is behind my choice pick of number 1 and he is now asking me if I want to pick door 2. Is he trying to completely throw me off, because he knows that my first choice is the right one or is he really trying to give me a second chance? Hmm,I don't really get the "puzzle" part of this question but I'm gonna go with my "gut" instinct and stay with door 1. How's that?
The puzzle part, Mel, is for you to figure out whether you have better odds by sticking with your first choice or changing doors. I'll post the correct answer tomorrow afternoon.
Ok, so I think I've got it. I think you will double your chances of winning if you switch doors. That is a "Byrd" graduate's answer to this question. Did I pass?
You know reading all these comments is hilarious....the time that it has taken Melissa to decide whether or not she is going to stick with door number one is the amount of time it is taking them backstage to get the goat ready to move behind whatever door she picks! Since I think that is what they are doing....moving the goat around...I don't think your chances are any better....and I agree with dad....who got me on this dumb gameshow?
Well...I would say that since there is a car behind one door and a goat behind the other door, I have a 50/50 chance to win the car no matter if I stay with door 1 or change to door 2..........
Michael, pick a better puzzle next time. Something cool like the snail one. Who picked that one again?
The correct answer is that you are better off changing doors.
Remember that your original choice of doors was independent of any other actions and it remains independent of the host's act of opening a door. That means that you had a 1/3 chance of being right when you picked the door and that you still have a 1/3 chance of being right after he opens a door with a goat behind it.
The host's action of opening a door is dependent on your first choice, and changing your original choice is dependent on the host's action. Given that only two options remain after the host opens a door, and that the probability of winning must add up to 1 (100%), your probability of winning if you change doors is 1-1/3=2/3.
Mel is correct, your chances are doubled if you change doors.
Well, I disagree. When Bob Barker reveals the goat behind door 3 and asks you if you want to pick another door, the whole odd game changes. Like starting over. Now the new odds game is only between two doors, thus you now have a 50/50 chance to win regardless of your choice of doors. There is no advantage to changing your pick...So I AM RIGHT. Does anyone agree with me????
What you say seems correct intuitively, and you are correct if Bob Barker doesn't know where the car is located. In that case, his action is not dependent on yours, and he also has a 1/3 probability of revealing the car when he opens a door. In that case, your second choice is a 50/50 shot assuming that Bob didn't reveal the car. Given that the puzzle states that the host knows where the car is located, the host does not have any chance of revealing the car, and that makes all the difference in the math.
There are several good articles on the internet that discuss this in more detail than I. It's classically know as the "Monty Hall Problem." Check out http://math.ucsd.edu/~crypto/Monty/monty.html as a good example with an interactive program.
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