hkcchk

the answer should be 1/2.  It is because no matter what, the empty will be opened after your choice.  That means one of the empty door has been excluded.  The question is that the probablity of your first choice and second choice is the same that is 1/2 and they are independ.  The probability will not increase as you will not be able to choose the one to be opened with car !

I want to change me answer.  It should be 1/3.  It is because of in the first choice, the probability of selecting the door with car is 1/3.  After opened a empty door, the probability seems shifted to the rest of the two door to become 1/2 but the probability of your original choice is still 1/3.  So change of selection is a good decision.

To illustrate the answer more clearly. Say there are 10 doors.  You have made your selection and the probability to choose the one with car is 1/10.  The host opened the rest of 8 empty door.  If the selection remain unchange, the probability is still 1/10 as it does not change even some empty doors are opened.  So, change of selection is correct.  I support the brillant with IQ228.

[ Last edited by hkcchk on 2007-3-20 at 11:19 PM ]