I don’t know why but I was thinking about this great logic/probability problem today. Many have probably heard this before but I’m going to post it anyway. I think it’s a great problem and fun to use to confuse the hell out of people. Try not to Google for the answer because 1) it’s easy to find and 2) knowing the answer is only a fraction of what value is in this problem to begin with. I absolutely did not get it right the first time I heard it and furthermore people with PHDs were writing vehement arguments about why the originally proposed solution (by Savant) was incorrect. This was after they heard the alleged solution! But of course they were wrong. OK, here it goes.
Feel free to argue, comment, answer at will. If you know the answer and understand the reason behind it already please hold off until a number of gbfans get a chance to try it out. Please, please, please don’t spoil it by just going to wikipedia and pasting the answer/proof.
It depends. One of my biggest issues with this question and similar questions is they do not adequately describe the host’s behavior during this scenario.
Most people will argue the mathematical probabilities for their answers to this, but since the host of the show is presenting the scenario to the contestant, I raise the question of motivation. Why would they present the choice? What makes better TV? Someone that wins a car, or someone that would have won a car but changes their decision to a goat? And what costs the studio more money, a goat or a car?
When presented with this problem purely as a mathematical probability question, I’d switch my choice, because there is no human element in the equation. I won’t explain why though until others give their choices and explanations.
If this was really happening, I’d probably stick with what I originally chose, but once again, it depends on the behaviors of the host and perceived motivation behind the scenario in the first place.
How is there a wrong answer to this? It’s not a factual question so there is no right or wrong.
Unless the capitalization is intentional and the opened door actually revealed a GOAT ie: a Pontiac GTO so both the remaining doors have an animal behind them.
Either way the “question” is deliberately obtuse, I don’t get the point.
There is a right/wrong answer to this - I mean, we’re talking probabilities not absolutes so regardless of the decision made I will say it’s not 0.0 or 1.0 probability, it is somewhere in between.
Let me clarify, this is not a trick question. I’m not playing with words. A goat/GOAT/GoAt is an animal, which for all intents and purposes is an undesirable outcome for the contestant. 3 doors, 3 objects. 2 of the objects are goats. 1 object is a car. here’s one sample scenario
DOOR 1, DOOR 2, DOOR 3
goat, goat, car
Mburkit, sure if it was a scenario where the contestant was a poker player or something, could read people, and subsequently the host, then that could certainly play in, agreed. But again, this is a simple probability problem and there are no hidden probabilities involved. There’s only one correct answer based on the inputs. I think that’s where you landed after your comments, but just wanted to clarify that.
So the question should have been stated as “According to probability is it better for the contestant to keep the initial door picked or change their choice to the other door”. THAT is an actual question then. Just saying “would you change and why/not” makes it seem like a cheesey high-school english test essay question instead of the mathmatics problem it is.
I know, it’s like the second result that show up in Google if you type in “gameshow” and “probability.” At any rate if anyone is interested in working it out, hold off on watching the vid.
So then is it supposed to be a logic problem, a math problem or games theory? Purposefully asking an obtuse question obscures any conclusions you could draw from the answers.
Once the goat is revealed to be behind one of the unpicked doors, it is removed from the math problem. If you choose to include it, the original math problem becomes null and void.
I still fail to understand just why the odds are not simply one:two. The game show analogy for the math is misleading.
At the end of the day (in the game show scenario) you still have two doors with one car. That, inherently, means there’s a 50% chance of success or failure. The clip from “21” does a ■■■■-poor job of actually explaining the logic behind the “correct” decision.
The math is basically 1/3 choice (your initial decision) divided by 1/2 (what you are left with)= 2/3. The math fails to tell me just why picking one over the other results in a 2/3 benefit- why doesn’t staying with my initial decision give me a 2/3 chance of success?
By eliminating door #3 from being the correct choice you are removing it from being the correct choice… so there are only 2 correct choices. 1:2
