ravi wrote:
>
> lets say you chose door1.
> probability that the prize is behind door1 is 1/3, probability that its
> not is 2/3. if door3 is opened to reveal no prize, then it follows that
> the probability that its behind door2 is now 1-prob(door1) = 2/3 ;-).
> so, you would be smart to switch your choice to door2!
>
Doesn't this depend on the question you ask. The question asked above (after the opening of door 1) is "What is the probability for door 2?" But what if you asked, instead, "What is the probability of Door 3?" and the answer would be
prob 3 = 1-prob (door1) = 2/3.
So both door 2 and door3, depending on what question you ask, have a probability of 2/3????
Put another way, if Door 2 was red and Door 3 green, if you ask "What is the probability of the red door?" the answer is 2/3 red door (and hence 1/3 green door). But if you ask what is the probability of the green door, the answer is green door 2/3 (and hence 1/3 for red door).
Carrol
P.S. We are having fun -- but please note that confusions over probability are at the very heart of almost all "conspiracy theories." Such theories continuously assert that such and such a coincidence has a low probability, hence it can't be true, hence their favorite answer is true.
Carrol