The Great Monty Hall: A new perspective.

[Ghost Post]

Many people whine about this problem, I think for anyone who disagrees with the solution, they should change their perspective on the problem. Let's say we try this problem with ten doors, the routine is the same. I pick one door and Monty then reveals the contents of eight doors, leaving one for me to ponder. Now, instead of seeing the problem as two doors to choose from, you should see it as one door against nine. So the odds that the prize is behind one of those nine is 90%. Even if eight doors are opened, the one left still holds a 90% probability because it is a part of the original nine.

Another way to look at this is on a bigger scale, let's try infinity. Let's now say that you can pick one door out of an infinate number of doors. The probability of picking the right door can be expressed as a limit:
assume X is the number of doors availavle and the limit is the probability of picking the right door.

lim 1/X = 0
X-->infinity

The limit of 1/X as X approaches infinity is 0.
For those of you who are not familiar with calculus, it basically states that the probability of picking the right door out of an infinite amount of doors is zero because one divided by infinity is zero.
So if Monty were to now open every door but one, which one would you chose? The other one of course, since there was a zero percent chance that you could have picked the right one to begin with, even if it comes down to the two, you still could not have picked the right one because there was a zero probability for that to occur.

[Wonko the Sane]

You're wrong about one thing. The probability of you getting the right door is NOT zero. 1/infinite is undefinted. You cannot derive the answer to an undefined problem by using it's limit. You would say that if you tried increasingly large numbers of doors, then as the number of doors grew without bound, the probability of getting the prize on your first pick gets closer to zero. There is no such number as infinite, so you cannot use it as part of a numerical equation. You will never have a 0% chance of getting the right door on the first pick, but you can have a chance that is very close. However, the larger the number of doors, the better off you are by switching.

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It's not the size of the spork, it's whether or not it's made of #7 recyclable plastic.

[daniel801]

i see where this is going, but the probability that it's the first door instead of one of the rest is also 0 (for infinity).

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anger is a gift

[Mercuria]

isn't all this covered in the original monty hall thread?