Quote:
Originally posted by chodadog
See, when you first choose, there are 3 possible outcomes. A, B, or C. You have a 1 in 3 chance of picking the correct box.
However, once a box is removed on the condition that said box is not a prize winner, and then given the chance to swap your choice, there are now 4 possibilities.
Everything changes when the third box is removed. 3 has nothing to do with it anymore. You know have 2 boxes and 2 possible variations to each. A total of 4 possible outcomes.
To make my point more obvious, think about it like this. The third box does not matter. Just ignore it. It's a given that you will end up with 2 boxes, one of which is empty, and one of which contains the prize. So why not just start there? Start with two boxes. 1 in 2 chance.
I am 99% sure i've got this right.
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The third box DOES matter, that's the whole point...
But let's look at a bigger-sized example. Perhaps that will make it clear.
Imagine someone has 1000 marbles. One of them contains a diamond, 999 do not.
He says "I will let you pick 1 of my marbles, and after that, I will put aside 998 of my marbles that do not contain diamonds."
Independent of your choice, he will ALWAYS be able to put aside 998 marbles that do not contain diamonds.
You pick a marble, with a 1/1000 chance of getting the diamond.
Then, he says, "I will now put aside 998 of my marbles that do not contain a diamond."
Now, has your marble suddenly gone from a 1/1000 chance of being a diamond to a 1/2 chance of being a diamond?
Even if, have you picked any of the non-diamonds, this very same thing would have happened?