So last night, Nik, Max, and I were studying for the philosophy midterm, and we got to talking about the Monty Hall problem. It goes like this: you’ve got three doors, behind one of which is a fun prize, and behind the other two are nothing. You guess one of the doors, in an attempt to obtain the awesome reward, but before you get to see if you were right or not, some punk named Monty opens a different door, and shows you that there is nothing behind it. You then have the opportunity to change your selection. What do you pick?
Well, we figured, being shown that another door has nothing behind it doesn’t change what your original choice was, so it doesn’t make a difference as to which door you pick now. Either of the remaining two doors will be equally likely to have the prize behind it, right?
Nope, I was wrong.