Could someone explain this solution please?

  • Thread starter mewmew
  • Start date
  • #1
114
0
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:

Answers and Replies

  • #2
quasar987
Science Advisor
Homework Helper
Gold Member
4,784
18
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.
 
  • #3
114
0
Thanks, that makes it much clearer.
 

Related Threads on Could someone explain this solution please?

Replies
2
Views
845
  • Last Post
Replies
1
Views
1K
Replies
1
Views
1K
Replies
2
Views
1K
  • Last Post
Replies
5
Views
2K
Replies
1
Views
2K
Replies
6
Views
5K
Top