On Sat, Feb 23, 2002 at 12:30:49PM +0100, Richard Baker wrote:
> If you're taken into the room, what is the probability that you get
^^^^^^^^^^^^^^^^^^^
> out alive?
I have to disagree with Alberto's interpretation. The question clearly
states that you're taken into the room.
> Argument 1. You are killed if two sixes are thrown. This happens 1 in
> 36 times. Therefore your chance of getting out alive is 35/36 = 97%.
This is the answer, by definition of probability. Given that you are
taken into the room, and the dice are cast, the probability you get out
is 35/36.
> Argument 2. Most people who are taken into the room are killed,
> therefore you are very likely to die. For example, suppose the third
> batch are killed. Then 100 people who go into the room die and 11
> survive. The chance of getting out alive is then 11/111 = 9.9%.
> (Working out the true probability is left as an exercise.)
Note that this argument does not answer the question that was
posed. This argument is considering people who haven't yet been taken
into the room. If you don't see that, ask yourself how you can talk
about batches of people, some being in the room and some waiting their
turn, without considering people outside the room.
If the question asked, "given an infinite sequence of people
(1,2,3,4...), who are queued up to get into a room....what is the
probability that person N does not get killed?" then Alberto's solution
looks correct to me.
--
"Erik Reuter" <[EMAIL PROTECTED]> http://www.erikreuter.com/
