CONCEPT
I’m posting this half in the hope that I get shot down so eloquently that the last decade of doubt on this issue is put eternally to rest. I don’t buy the textbook explanation of the Monty Hall problem, and here’s why:
1. The explanation assumes that switching doors amounts to taking in 2 out of 3 possibilities where one will yield a prize (corresponding to a 2 in 3 chance of success). The explanation assumes one choice with a 1 in 3 chance of success. But there are two choices, and there is no reason why the statistical fallous of the first should be applied to the second.
The first choice is to select a door with a 1 in 3 chance of success. There is no (practical) consequence of this choice; it’s like when Howie Mandel ratchets up the tension on Deal or No Deal by pinching someone’s gut or throwing a Hummer up on the screen.
The second choice is to select a door with a 1 in 2 chance of success. One can choose the same door (#1 or #3) or a different door (#3 or #1), with the consequence of determining if one has won the price.
I think it’s erroneous, then, to statistically consider this a one one-in-three. It’s an applied question in the sense that the process of resolving the question is interrupted and relevant information revealed. The fact that a choice follows has the effect of restarting the problem from square one. Statistically, there is a one-in-two chance regardless of the door chosen.
2. For some reason it’s portrayed as a compelling argument that the host reveals there is nothing behind one of the other doors. Since there is nothing behind at least two doors, the host can open a door with the same result (revealing nothing) regardless of whether I select door #1, #2, #3. The host need not even know what door the prize is behind in order to reveal a door without a prize behind it. (Again, Howie Mandel).
Is the earth shaking with the force of what I’ve just revealed?
Or, as I suspect is the case, am I totally missing the point?
And if it’s the latter, is anybody willing to make clear, once and for all, the flaw in my logic?
END OF POST.