This is from Feynman's lectures:
We may often wish to ask the following question: “What is the chance that a molecule will experience a collision during the next small interval of time dt?” The answer, we may intuitively understand, is dt/τ. But let us try to make a more convincing argument. Suppose that there were a very large number N of molecules. How many will have collisions in the next interval of time dt? If there is equilibrium, nothing is changing on the average with time. So N molecules waiting the time dt will have the same number of collisions as one molecule waiting for the time Ndt. That number we know is Ndt/τ. So the number of hits of N molecules is Ndt/τ in a time dt, and the chance, or probability, of a hit for anyone molecule is just 1/N as large, or (1/N)(Ndt/τ)=dt/τ, as we guessed above. That is to say, the fraction of the molecules which will suffer a collision in the time dt is dt/τ. To take an example, if τ is one minute, then in one second the fraction of particles which will suffer collisions is 1/60. What this means, of course, is that 1/60 of the molecules happen to be close enough to what they are going to hit next that their collisions will occur in the next second.
So basically this is what I want to understand, but I still don't...
So basically he says that the number of hits for N molecules in time dt is Ndt/τ, but then he says the probability of a hit for one molecule is 1/N as large, which is dt/τ. How is this? Surely 1/N multiplied by the number of hits for N molecules is average number of hits for one molecule in time dt, not the probability of a single hit.