Three doors question:
Created | Updated Jan 28, 2002
Suppose you are in a game, and you are presented with three doors. One of these doors hides a huge prize, the others are empty.
After you have chosen one door, the gamehost will not immediately show you what's behind your door, but in stead, he will open one of the others, to show that the prize is NOT there.
Then you are allowed a choice: stay with your original choice or switch?
There are people who keep saying that you must switch...
I'll simply list here all possible sequences of events, showing that the outcomes is NOT in favor of switching doors after the first round.
Obviously, from the above follows that the gamehost can NOT:
1. directly open the door you selected.
2. open the door where the prize is.
So, if you choose wrong, there's only ONE door he can open. But if you choose right at the start, he has TWO possibilities. Below are ALL the possible sequences:
Prize behind A, you choose A, gamehost discards B -> switch to C - lose
Prize behind A, you choose A, gamehost discards C -> switch to B - lose
Prize behind A, you choose B, gamehost discards C -> switch to A - win
Prize behind A, you choose C, gamehost discards B -> switch to A - win
Prize behind B, you choose A, gamehost discards C -> switch to B - win
Prize behind B, you choose B, gamehost discards A -> switch to C - lose
Prize behind B, you choose B, gamehost discards C -> switch to A - lose
Prize behind B, you choose C, gamehost discards A -> switch to B - win
Prize behind C, you choose A, gamehost discards B -> switch to C - win
Prize behind C, you choose B, gamehost discards A -> switch to C - win
Prize behind C, you choose C, gamehost discards A -> switch to B - lose
Prize behind C, you choose C, gamehost discards B -> switch to A - lose
If you carefully apply statistics, you will find ALL possibilities above, and you will also note that your chances are EVEN AT ALL TIMES!
Whoever thinks they can prove me wrong, better take some basic math classes. :-)
After you have chosen one door, the gamehost will not immediately show you what's behind your door, but in stead, he will open one of the others, to show that the prize is NOT there.
Then you are allowed a choice: stay with your original choice or switch?
There are people who keep saying that you must switch...
I'll simply list here all possible sequences of events, showing that the outcomes is NOT in favor of switching doors after the first round.
Obviously, from the above follows that the gamehost can NOT:
1. directly open the door you selected.
2. open the door where the prize is.
So, if you choose wrong, there's only ONE door he can open. But if you choose right at the start, he has TWO possibilities. Below are ALL the possible sequences:
Prize behind A, you choose A, gamehost discards B -> switch to C - lose
Prize behind A, you choose A, gamehost discards C -> switch to B - lose
Prize behind A, you choose B, gamehost discards C -> switch to A - win
Prize behind A, you choose C, gamehost discards B -> switch to A - win
Prize behind B, you choose A, gamehost discards C -> switch to B - win
Prize behind B, you choose B, gamehost discards A -> switch to C - lose
Prize behind B, you choose B, gamehost discards C -> switch to A - lose
Prize behind B, you choose C, gamehost discards A -> switch to B - win
Prize behind C, you choose A, gamehost discards B -> switch to C - win
Prize behind C, you choose B, gamehost discards A -> switch to C - win
Prize behind C, you choose C, gamehost discards A -> switch to B - lose
Prize behind C, you choose C, gamehost discards B -> switch to A - lose
If you carefully apply statistics, you will find ALL possibilities above, and you will also note that your chances are EVEN AT ALL TIMES!
Whoever thinks they can prove me wrong, better take some basic math classes. :-)
