# 4: Fundamental 2 - Counting Configurations

• • Contributed by Andrea Allgood Carter
• Assistant Professor of Chemistry (Department of Chemistry, Physics, and Geoscience) at Meredith College

• 4.1: The Distribution Function as a Summary of Experimental Results
As we collect increasing amounts of data, the accumulation quickly becomes unwieldy unless we can reduce it to a mathematical model. We call the mathematical model we develop a distribution function, because it is a function that expresses what we are able to learn about the data source—the distribution. A distribution function is an equation that summarizes the results of many measurements; it is a mathematical model for a real-world source of data.
• 4.2: Outcomes, Events, and Probability
We also need to introduce the idea that a function that successfully models the results of past experiments can be used to predict some of the characteristics of future results.
• 4.3: Some Important Properties of Events
If we know the probabilities of the possible outcomes of a trial, we can calculate the probabilities for combinations of outcomes. These are based on two rules, which we call the laws of probability. If we partition the outcomes into exhaustive and mutually exclusive events, the laws of probability also apply. Since, as we define them, “events” is a more general term than “outcomes,” we call them the law of the probability of alternative events and the law of the probability of compound events.
• 4.4: Applying the Laws of Probability
The laws of probability apply to events that are independent. If the result of one trial depends on the result of another trial, we may still be able to use the laws of probability. However, to do so, we must know the nature of the interdependence.
• 4.5: Combinatorics and Multiplicity
Combinatorics is the branch of math related to counting events and outcomes, while multiplicity is the statistical thermodynamics variable equal to the number of possible outcomes.  They are intricately connected.