On Sat, Feb 23, 2002 at 10:58:08PM -0000, Alberto Monteiro wrote: > Ok, let me re-state the pseudo-paradox. > > One person enters a room. Now a loop begins: > 2d6 are rolled, and if it gets 12, everybody in the > room is killed, and the experiment ends. Otherwise, > those people in the room become free, and 10x their > number enter the room. > > For any person that entered the room, what is the > probability that he left it alive?
> For each number F - the index number of the firing of the machine > gun - there is a different survival probability for the people that > entered the room, namely, the number of people that entered the room > in the earlier rounds divided by the total number of people that > entered the room. The survival probability of the people that have entered the room is always the same: 35/36. It cannot be otherwise, by definition. > >It seems to me that the group you are calculating the survival > >probability of is changing from line to line. > > It is. For each F >= 2, the "universe" grows by k^(F-1), while the set > of people that survived grows by k^(F-2) I don't think this is a well-defined system. It is strange to calculate the survival probability of a group that is a different group than it was before. > The N-th person in the queue can only be killed if > (1 + F + F^2 + ... + F^(N-2)) < N <= (same sum) + F^(N-1) > > Explicitly, for each N the killing number F is: > N = 1 -> F = 1 > N = 2 -> F = 2 > up to N = 11 -> F = 2 > N = 12 to N = 111 -> F = 3 > etc This is just mathematical definitions of 1, 11, 111, .... But I think the answer to my question is that you aren't calculating the probability of a specific group in the sequence, but rather some strangely varying group. It looks like an ill-defined system to me. > But this is a different problem, namely: what is the chance that > the N-th person of the queue will survive? Yes, that is what I was answering. I don't think you can clearly define what you are answering. You said you did, but I don't think you did. > Yes - as I did in the introduction. I don't think so. Maybe you should try to say it more explicitly. -- "Erik Reuter" <[EMAIL PROTECTED]> http://www.erikreuter.com/
