Introduction to Probability

In chapter 5 we begin the study of probability, needed for inference in the process of statistics. It is a bit of a departure from what we have studied in chapters 1 through 4. But don’t worry, concepts such as mean, standard deviation, and shape of a distribution will return in chapter 6. But for now, we will focus on the concept of probability.

The process of statistics

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We will discuss basic probability and the three approaches to finding it in section 5.1. The rest of the chapter will involve finding the probability that at least one of two outcomes occurs (section 5.2), or that both outcomes occur (section 5.3) or that one will occur if we know the other already occurred (section 5.4).

By the end of this chapter, you will be able to:

•Identify three approaches to probability.

◦Classical (or theoretical)

◦Empirical (estimated from data)

◦Subjective

•Find empirical probability from tables and data.

•Describe sample spaces for simple experiments.

•Apply the addition rule for multiple events.

◦For mutually exclusive events

◦For non-exclusive events

•Use the complement rule.

•Apply the multiplication rule.

◦For independent events

◦For dependent events

•Understand Two-way tables and calculate probability from them.