So anyone who knows me knows that I love Wikipedia. Recently I have been researching paradoxes. Here's an interesting one for you guys to wrap your head around
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it seems like it could go either way. his chances are 1/3 at the beginning. after the host opens a door revealing a goat it would seem as though his chances are 1/2, which isn't doubling by any means.
to double he'd have to go from 1/3 to 2/3, so i'm pretty sure the answer has to do with still considering the open door with the goat as part of the general equation. the contestant chooses a door - his chances are 1/3. the chance the car is behind one of the two remaining doors is 2/3, assuming the car is placed at random. when the host opens a door with a goat behind it, the 'odds' behind the third (closed) door now double to 2/3, and therefore switching doors doubles your odds.
i'm not sure if this is an 'honest mathematical truth', though, for some reason.
After the doors are switched, the odds of getting the car are doubled from 1/3 to 2/3. Believe it or not, the odds are never 1/2 at anytime. After the first goat is revealed, the odds are still 1/3 (because you don't know which goat it is). Switching increases it to 2/3.
The mathematical reasoning is pretty drawn out and complicated, but it makes perfect sense. Check the wikipedia article if necessary. it's called the Monty Hall problem or something.
i would guess that its because the first time he has a 1 in 3 chance, and the second time he has a 1/2 chance... is that it??????????????????????????????
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it seems like it could go either way. his chances are 1/3 at the beginning. after the host opens a door revealing a goat it would seem as though his chances are 1/2, which isn't doubling by any means.
to double he'd have to go from 1/3 to 2/3, so i'm pretty sure the answer has to do with still considering the open door with the goat as part of the general equation. the contestant chooses a door - his chances are 1/3. the chance the car is behind one of the two remaining doors is 2/3, assuming the car is placed at random. when the host opens a door with a goat behind it, the 'odds' behind the third (closed) door now double to 2/3, and therefore switching doors doubles your odds.
i'm not sure if this is an 'honest mathematical truth', though, for some reason.
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The mathematical reasoning is pretty drawn out and complicated, but it makes perfect sense. Check the wikipedia article if necessary. it's called the Monty Hall problem or something.
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