Could someone explain this solution please?

  • Thread starter mewmew
  • Start date
  • Tags
In summary, the conversation discusses the probability, P(N), in a given volume V for a certain number of molecules N. The probability is derived from the expression p=V/V0, where p represents the probability that one molecule is in V and q represents the probability that it is somewhere else. The conversation then goes on to explain how the probability of N particles being in V and the rest not being in V is calculated by multiplying p^N and q^(N0-N) and then summing over the possible ways to choose N particles among N0. Finally, the conversation touches on basic probability results and how the probability is ultimately calculated.
  • #1
0 [Broken] [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:
Physics news on
  • #2
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
Thanks, that makes it much clearer.

1. What is the purpose of this solution?

The purpose of this solution is to provide a clear and concise explanation of a concept or problem.

2. Who is the intended audience for this solution?

The intended audience for this solution is anyone seeking clarification on a particular topic or problem, regardless of their level of knowledge or expertise.

3. How is this solution structured?

This solution is typically structured with a brief introduction to the topic, followed by a step-by-step explanation of the solution, and ending with a conclusion or summary.

4. Are there any visual aids or examples included in this solution?

Yes, this solution may include visual aids such as diagrams, graphs, or examples to further illustrate the concept or problem.

5. Is this solution reliable and accurate?

As a scientist, I strive to provide accurate and reliable information in all of my solutions. However, it is always important to critically evaluate and verify any information, including this solution, before applying it to your own work.

Suggested for: Could someone explain this solution please?