Your "Paradox" is really a play on words, or an ill-defined question.
Richard Baker wrote: > > There is a room with a machinegun and a guy with two dice. A person is > taken into the room and the dice thrown. If they come up with two sixes > then the person is shot. Otherwise he or she is let out and a group of > ten people brought in. Again the dice are thrown and if they both come > up sixes then the people are shot. Otherwise a group ten times bigger > is brought into the room. This "game" goes on until a group is shot. > (There is an infinite supply of people. Nobody goes into the room > twice.) If you're taken into the room, what is the probability that you > get out alive? > > 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 true answer to the question at the end of the game. **IF YOU ARE TAKEN INTO THE ROOM,** the odds of getting shot at that time are 1/36. > 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.) This is really the answer to the question: "If your friend was one of the subjects, what are the odds that (s)he survived?" (11/111) If you ask the same question about yourself, the odds would necessarily be 1/1, since you couldn't ask/answer such a question while dead. If you want to know your chances for survival before the experiment, then it gets much more complicated, as the experiment ends once someone gets shot. You would very likely be in the pool of people waiting to go into the room at the end of the experiment. (take the example for #2: If they had 11,111 people on hand for the experiment, and it ended with 100 dead, your odds of survival would be 11011/11111, or 99.1%. If you assume an infinite supply of subjects, then the odds of any random subject dying would be virtually zero (a finite number divided by an inifinite number = 0) -- Matt _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at http://mail.yahoo.com
