An Interesting Idea at the Foundation of Probability

We have been looking at a situation in which many molecules are moving around randomly over a long period of time. In this situation we can talk about two distinct but related ideas.

• We can choose a random molecule and ask about the probability that it is found in a particular cell at a particular time.

• We can pick one particular time and ask about the fraction of the molecules found in a particular cell at that time.

In this situation these two ideas yield the same answer -- that is, the probability that a molecule chosen at random at a given time is found in a particular cell is the same as the fraction of molecules in that cell at that time.