I suck at explaining stuff. Recently, a friend asked me a quite well known probability problem:

Suppose you are playing a TV game show and the final prize is a car. Its hidden behind one of the three doors, the other two doors hide nothing. The game show host, who knows which door hides the car asks you to choose a door and if you choose the one with the car, you get the car. Otherwise you end up with nothing.

Lets say the Doors are labeled 'A', 'B' and 'C'. You randomly choose door 'B'. The hosts then proceeds to open door 'A' and you see its empty. Now, the host asks you whether you want to change your option to Door 'C' or hold your pick. What should you do?

The answer to this question is:

I am going to put it in spoilers for anyone who wants to solve it.

! Switching would improve your odds, so you should.

! How it works is that when he opened the door containing nothing he eliminated one of the options and out of the two doors remaining one contains the car. If you picked the wrong one before, switching would get you the car and vice versa. Since there was a 66% chance you chose the wrong door when he asked you to pick one the first time and 33% you picked the right one, switching now would give you twice as better odds then if you didn't switch.

Now, here lies the problem:

! After I solved this question and asked my cousin, he went on a rant that after one of the doors was opened, the remaining doors each have a probability of 50% and that "A dice has no memory".

Anyway, I have until tomorrow to come up with an example to explain this to him and I can't think of any. So, help anyone?