Originally Posted by
Flynbuy 
Just can't wrap my brain around it.......
So, if you started with a 1 in a 100 or 1% chance and took out 98 empty boxes, I just cannot see that the probability now isn't 1 in 2 or 50% and switching doesn't matter?!?!? How can then switching based on events that have already transpired affect the outcome of the draw????
Why is it any different than simply saying I have two boxes and one has money in it. Isn't the probability at that point 1 out of 2 regardless of switching ones choice or not???
The other way of looking at it is that your chances have improved because many of the empty boxes have now been taken away, or 1 prisoner not being pardoned has now been taken away.
-100 boxes - 1 in 100 chance
-50 boxes - 1 in 50 chance
-2 boxes - 1 in 2 chance
That improvement in chance has to be factored into the equation when mathematicians do their fancy calculations.
Starting with only 2 boxes can't be the same as starting with 100 boxes and then switching your first choice with 1 of the final 2 boxes, it can't both be 50% because at the start there was a 1 in 100 chance rather than a 1 in 2 chance!!
So start with a 1/100, take out 98 boxes can't equal the same as simply starting with 2 boxes to begin with, which is a 1/2.
Probability surely needs to reflect the increase in probability, or the change in probability somehow with numbers, even though the options, number of boxes, number of prisoners remains the same!!