1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Could someone explain this solution please?

  1. Nov 8, 2006 #1
    http://img478.imageshack.us/img478/5606/part1bd8.jpg [Broken]
    http://img183.imageshack.us/img183/686/part2yu0.jpg [Broken]

    We got this in class from a TA and the professor is in China and not able to answer questions. I am confused by where the probability,P(N), comes from in part a. It looks like a multiplicity multiplied by some other stuff but I don't understand it at all. I haven't had any probability/statistics but I assume it's pretty basic. If anyone could help me understand how this probability comes about it would be much appreciated. Thanks
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Nov 8, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    p=V/V0 is the probability that one molecule be in the volume V. q=1-p is the probablity that it be somwhere else. This expression of q comes from the fact that since the particle must be somewhere we must have p+q=1.

    Choose N particles among N0. The probability that these N be in V and that the rest of them are NOT in V is [itex]p^Nq^{N_0-N}[/itex]. In general, the probability that exactly N particles be in V and the rest not in V is [itex]p^Nq^{N_0-N}[/itex] summed over as many ways there are to choose which N particles among N0 are going to be in V. And you probably at least know some basic probability results, among which that the number of ways to chose N amongst N0 is [tex]\binom{N_0}{N}=\frac{N_0!}{N!(N_0-N)!}[/tex]

    So we have the result.
  4. Nov 8, 2006 #3
    Thanks, that makes it much clearer.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook