Probability theory plays a central role in statistics. After all, statistical analysis is applied to a collection of data in order to discover something about the underlying events. These events may be connected to one another—for example, mutually exclusive—but the individual choices involved are assumed to be random. Alternatively, we may sample a population at random and make inferences about the population as a whole from the sample by using statistical analysis. Therefore, a solid understanding of probability theory—the study of random events—is necessary to understand how statistical analysis works and also to correctly interpret the results.

You have an intuition about probability. As you will see, in some cases, probability theory seems obvious. But be careful: Occasionally, a seemingly obvious answer will turn out to be wrong—because sometimes your intuition about probability will fail. Even in seemingly simple cases, it is best to follow the rules of probability rather than rely on your hunches.