Probability Of No Meeting!

I didn't really wnat to cross-post this, so I just copied it over to rsa. I
think it is a topic of recent interest.

"Patrick D. Rockwell" wrote in message
...
As I'm sure many of you know, if N people, each of whom are willing
to wait d amount of time (where d is a fraction of the time span that
they arrive between) agree to meet each other in a specified time
range, and their arrival times are randomly distributed, then the
probability that ALL of them meet is

P(ALL)=n*d^(n-1)-(n-1)*d^n

and the probability that NONE of them meet is given by

P(NONE)=(1-(n-1)d)^n

Awhile back, I posed the question of what is the probability that ALL
meet if each has a different waiting time, and what is the probability
that NONE of them meet.

one person was able to compute for me the probability that ALL meet
and put his answer in a PDF file which can be found here.


http://webpages.charter.net/smithabi...babilities.pdf


A few years earlier, someone else gave me a formula for P(NONE) if all
of the waiting times were different. I don't remember it all. I recall
something like


P(NONE MEET)=Product(1-S)^N Where S=Sum(d_k)
j=1 to N K=1 to
N

for Kj

This is if N people agree to meet, but the above formula doesn't
compute for the simple case of N=2, and say, d_1=.1 and d_2=.25.

I seem to recall that the formula was really

Product(1-S+(something else))^N
j=1 to N with S defined as above.

but I don't recall what that something else was. Does anyone want to
tackle this?

--
Patrick D. Rockwell