Many things in physics require the mathematical use of probability. One area for which our understanding is based on pure probability is radioactive decay.
Although one cannot be sure about the outcome of a single event when it depends upon probability, the calculation of the probability of a specific outcome is a precise mathematical process. For independent events, the probability is described by the binomial distribution.
For physical applications, the binomial distribution is often inconvenient because it contains the factorials which are hard to manage when the number of events is large. From the behavior of gas molecules to the processes of radioactive decay or nuclear scattering, the numbers are very large indeed. Two approaches to probability can be used in place of the binomial distribution in physical settings. When the number is very large, then the binomial distribution can be approximated by a Gaussian distribution. In other physical cases where the probability for a given event is very small, the distribution can be approximated by a Poisson distribution.
In dealing with molecular distributions, the Maxwell speed distribution is an important element. Kinetic theory also gives us a development of the mean free path of molecules. Together they can give us a means for calculating the frequency of molecular collisions.
Another application of molecular distributions is the Barometric formula, which allows us to predict the change in atmospheric pressure with height.
Homework set #2