Chapter 18

Introducing Probability


Defining probability

Working with probability

Dealing with random variables and their distributions

Focusing on the binomial distribution

Throughout this book, I toss around the concept of probability because it’s the basis of hypothesis testing and inferential statistics. Most of the time, I represent probability as the proportion of area under part of a distribution. For example, the probability of a Type I error (a.k.a. α) is the area in a tail of the standard normal distribution or the t distribution.

In this chapter, I explore probability in greater detail, including random variables, permutations, and combinations. I examine probability’s fundamentals and applications and then zero in on a couple of specific probability distributions. Then, after telling you about probability concepts, I discuss probability-related Excel worksheet functions.

What Is Probability?

Most of us have an intuitive idea about what probability is all about. Toss a fair coin and you have a 50-50 chance it comes up “heads.” Toss a fair die (one of a pair of dice) and you have a one-in-six chance it comes up “2.”

If you wanted to be more formal in your definition, you’d most likely say something about all the possible things that could happen, and the proportion of those things you care about. Two things can happen when you toss a coin, and if you only care about one of them (heads), the probability of that event happening is one out of two. Six ...

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