You are shown three boxes, and told that one of them contains a prize. You are then asked to pick one box, and if that box is the one with the prize, you will win it. After picking a box, you are shown that one of the other two boxes is empty, and offered a chance to change your selection.

Should you do this? Would changing your choice to the other remaining box affect your odds of winning? Why or why not?

I don't think you should change your selection because the boxes are
independent of each other . However, your chances do increase,
but they don't increase because you suddenly decide to pick up the
other box. Example: You first select box A. Because there
are 3 boxes total, you have 1/3 chance of winning, and 2/3 chance of
losing. Then box C is shown to be empty. Suddenly there are
only two boxes (A and B) that have a possible winning. Thus, you
now have 1/2 chance of winning and a 1/2 of losing. These odds
will not increase if you decide to select box B instead of A, for there
are still two boxes, each possible of yielding a win.

*Edited on ***May 2, 2004, 8:59 pm**