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Could someone explain this solution please?

  1. Nov 8, 2006 #1

    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
  2. jcsd
  3. Nov 8, 2006 #2


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    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.
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