another puzzler
Dave Platt wrote:
In article ,
Bill Graham wrote:
I claqim there are two games. In the first game, you go to the
studio, pick a door, and then go home to wait and see if they call
you and tell you that you either won or lost. Your odds are only 1/3
of winning this game. But if you play the second game, then you go
to the studio and mess around until the host opens up a door and
shown you the donkey behind it. then you can play the game with
50-50 odds of winning. The only thing I have trouble explaining is
why, in order to play this second game with the better odds, you
have to switch doors. But, in fact, you do have to switch in order
to switch games and take advantage of the better odds.
Yup.
The distinction between the two games is based on the amount of
information available to you at the moment you make your final
decision.
In the first game, the only information you have is that every door
available to you to choose has a 1/3 chance of being correct.
In the second game, additional information is given to you by the
host, after you make your initial decision and before you make your
second one. "The prize is *not* behind that door over there."
Actually, you don't *have* to switch doors to "play the second game".
You're playing it from the moment the host gives you this extra
information. It's just that if you ignore this extra information, and
*think* you're still playing the first game (as many people do), you
are more likely than not to make a poor choice in the decision you
make in this second game.
Suppose for the moment that there are two contestants. One picks door two,
and the other picks door one. Then the moderator opens door three and shows
everyone that there is a donkey behind that door. Now, will it make any
difference if the other two switch their initial picks or not? And, if they
do swap doors, with they both enjoy a 2/3 chance of winning?
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