The New Critical Thinking by Jack Lyons & Barry Ward

Author:Jack Lyons & Barry Ward
Language: eng
Format: epub
Publisher: Routledge

Chapter 6

Probability and Frequency

We all intuitively know what it means to say that one event is more probable than another. On a day when there are lots of dark clouds overhead, we know that rain is more probable or more likely than on days when the sky is blue and when the weather is warm and mild. We know that if we come in contact with people who have the flu that raises the probability that we will contract the flu. Also, you intuitively understood what we meant in Chapter 4 when we said that an inductive argument is one whose premises render its conclusion probable: the more probable something is, the more it is to be expected.

Probability theory has developed from its roots in attempting to gamble better, into a highly abstract area of mathematical research. But you don’t need to be a mathematician to understand the probabilities that we encounter in everyday life. So our approach will be pretty much the one we took to validity in Chapter 2. Just as you already had the ability to distinguish good arguments from bad before you ever opened this book, you also know a significant amount about probability, even if you never took a math course on the subject. Our goal is to harness and sharpen that understanding as effectively as possible. Crucially, we want to give you a good feel for assessing probabilistic arguments without the need to understand anything more complicated than basic arithmetic: addition, subtraction, multiplication, and division. On the other hand (surprise surprise!), System 1 doesn’t handle certain kinds of probabilistic judgments very well. So, as with deductive logic, we’ll have to flag those places where our intuitive processor leads us astray. What we will do in this chapter is provide some easily mastered, psychologically sound, informal methods for making good sense of probabilistic information.

We’re going to do some math in this chapter. But even if you hate math and are sure you’ll never actually calculate probabilities on your own accord, please bear with us. It turns out that there are some very surprising and hugely important facts about probability which you won’t be able to fully appreciate without walking through the math, but which will offer useful take-home lessons that won’t require you to do the math again. At the same time, you’ll have learned some mathematical tools that will allow you to calculate probabilities if you want.

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