Originally posted by wittywonkaThere are other threads on this subject, but it basically boils down to the fact that the "host" always opens a door with nothing in it.
Could someone please explain to me the concept behind the following problem:
You're on a gameshow and you have to choose between three doors A, B, and C, one of which has a car behind it. You choose door C, but instead of the gameshow host's showing you whether you were correct, he opens door A and shows you that it has nothing behind it, and lets you ...[text shortened]... ng a combination of the two, but I simply don't get it.
Thanks in advance for your time.
Originally posted by forkedknightThat concept actually makes some sense, about expanding your initial game field to 100 doors, but where did you get that formula for the probability after switching? Taking the 100 doors scenario, wouldn't it be .01 probability (staying with the door you chose originally) and .5 probability (switching)?
There are other threads on this subject, but it basically boils down to the fact that the "host" always opens a door with nothing in it.
If you expand it out to 100 doors, where you choose one and the host opens 98 doors with nothing in them, it becomes more apparent that if you stick with your door, you have your original odds (1/n), but if you switch, your odds become (1 + number of opened doors)/(n - number of opened doors)
Originally posted by PalynkaOf all the explanations I've heard of why you should always switch, this is the most straightforward. Not sure why I've never seen it before now.
I usually use the example forkedknight gave, but if you want another way of thinking about it is to think about the probability of winning by NOT switching in a sort of frequentist way (imagine you repeat the experiment many times).
If you NEVER switch, then how many times will you win? Exactly 1/3 of the times.
If you ALWAYS switch, then how many times ...[text shortened]... PS: All this is again assuming he always opens a door without a prize as other comments mention.