Quote:
Originally Posted by therusty
I always hated the Parade answer and I don't like the Wiki answer any better. The way I see it there are 24 possible scenarios:
Prize behind door1, you pick door 1, monty reveals door 2, you keep=you win
Prize behind door1, you pick door 1, monty reveals door 2, you switch=you lose
Prize behind door1, you pick door 1, monty reveals door 3, you keep=you win
Prize behind door1, you pick door 1, monty reveals door 3, you switch=you lose
Prize behind door1, you pick door 2, monty reveals door 3, you keep=you lose
Prize behind door1, you pick door 2, monty reveals door 3, you switch=you win
Prize behind door1, you pick door 3, monty reveals door 2, you keep=you lose
Prize behind door1, you pick door 3, monty reveals door 2, you switch=you win
If you put the prize behind doors 2 and 3 and repeat the exercise, you get 8 more outcomes apiece identical to the above 8 (4 scenarios for picking the right door and 4 for picking the wrong door) to total 24 outcomes, with 12 switches winning and 12 losing.
That makes the odds 5050.

the door number/order is irrelevant, basically this is what you said in terms of goats and a car (keeping the same order as you):
pick car, monty shows goat1, you keep => you win
pick car, monty shows goat1, you switch => you lose
pick car, monty shows goat2, you keep => you win
pick car, monty shows goat2, you switch => you lose
pick goat1, monty shows goat2, you keep => you lose
pick goat1, monty shows goat2, you switch => you win
pick goat2, monty shows goat1, you keep => you lose
pick goat2, monty shows goat1, you switch => you win
BUT!!!!
the initial probability of picking the car (first group above) is 1/3
the initial probability of picking goat1 (second group) is 1/3
the initial probability of picking goat2 (thirs group) is 1/3
now lets say you always keep  you will win ONLY if you pick the car first  1/3 chance
if you always switch you will win only if you pick a goat first (any goat though, it's the interchangeable goats that make this problem
)  so if P(goat1) = 1/3 and P(goat2) = 1/3 then P(either goat) = 2/3
jinx