Re: Shooting room paradox

Jacob Costello (
Thu, 5 Dec 1996 18:35:05 -0600 (CST)

> Since 90% of the people who go into the room see double sixes, it follows
> that if you are a person in the room, the chances that you will see double
> sixes is 90%, far greater than the 1/36 chance we calculated before.
Let me stick my neck out and state the obvious.

I think all this means (according to classical probability) is that if
this experiment (an entire sequence of getting people and rolling and gettting
more people until the sixes are rolled being one experiment) is conducted an
infinite number of times, then any person will be in the room at the point the
sixes are rolled in 90% of the experiments. The underlying reason of course
is that more you have a higher probability of being in a large group than
a small group, a priori.
This is no contradiction to the 1/36 probability. Saying that there
is a 1/36 probability of seeing sixes if you are in presently in the room
refers to a different set of experiments, namely gathering a bunch of people in
a room and rolling the dice. In 1/36 of these (infinitely repeated)
experiments double sixes will be rolled (how many people are in the room is
irrelevant.) What has happened is we've gained more information. Before the
experiment starts we don't know which group we're in, but once we actually do
know the probability is 1/36.

jake costello