**Next message:**Harnad, Stevan: "Re: Monty Hall"**Previous message:**Taylor, Karl: "Re: Monty Hall"**Maybe in reply to:**Lowing, Ben: "Monty Hall"**Next in thread:**Harnad, Stevan: "Re: Monty Hall"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Think about what the statement "there is a 1/3 probability of the first

door picked containing the prize" actually means, i.e. that in one out

of three occasions it will be the winning door. What do you suggest

happens on the opening of the empty door. There is no way this can

alter the probability of the prize being under the one picked since it

is already either there or not there, the probability of it being under

this door therefore must remain the same as before (1/3) you are

provided with the extra imformation, and as such the probability of it

being under the other door (the one you'd switch to) must be 2/3.

Probability of winning if you stick with original door;

pick 2, prize is under 1, you lose.

pick 2, prize is under 2, you win.

pick 2, prize is under 3, you lose.

pick 1, prize is under 1, you win.

pick 1, prize is under 2, you lose.

pick 1, prize is under 3, you lose.

pick 3, prize is under 1 , you lose.

pick 3, prize is under 2, you lose.

pick 3, prize is under 3, you win.

3/9 (1/3) chance of winning.

Probability of winning if you switch;

pick 1, prize is under 1, you lose.

pick 1, prize is under 2,

door 3 is opened and you are told it's empty, switch to 2, you win.

pick 1, prize is under 3,

door 2 is opened, you are shown it's empty, switch to door 3 you win.

pick 2, prize is under 1, door 3 is opened, you switch to 1, win.

pick 2, prize is under 2, you lose.

pick 2, prize is under 3, door 1 is opened, you switch to 3, win.

pick 3, prize is under 1, door 2 is opened, you switch to 1, win.

pick 3, prize is under 2, door 1 is opened, you switch to 2, win.

pick 3, prize is under 3,

you are shown either of the two empty doors, switch to other and lose.

i.e. 6/9 chance of winning or 2/3.

**Next message:**Harnad, Stevan: "Re: Monty Hall"**Previous message:**Taylor, Karl: "Re: Monty Hall"**Maybe in reply to:**Lowing, Ben: "Monty Hall"**Next in thread:**Harnad, Stevan: "Re: Monty Hall"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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