Originally posted by I am a fish
A similar problem is as follows:
There are three identical boxes, one of which contains a prize. You are asked to select a box. Before opening it however, one of the other boxes is
opened and revealed to empty. You are then given the option of changing your choice of box. What should you do to maximise your chance of winning?
The "obvious" answer is that switching boxes won't affect your chances of winning, as the game is entirely random. However this is
wrong. The probability that the prize is in one of the two boxes that you didn't initially choose is 2/3. Once one of the boxes is opened, this
probability remains the same and so there is still a 2/3 chance that the prize is in the remaining unselected box. Therefore, switching boxes doubles
your chance of winning. |