IN CHAPTER3 we began to make use of the concept of probability. For example, we saw that
about 19% of children have Behavior Problem scores between 52 and 56 and thus con-
cluded that if we chose a child at random, the probability that he or she would score be-
tween 52 and 56 is .19. When we begin concentrating on inferential statistics in Chapter 6,
we will rely heavily on statements of probability. There we will be making statements of
the form, “If this hypothesis were correct, the probability is only .015 that we would have
obtained a result as extreme as the one we actually obtained.” If we are to rely on state-
ments of probability, it is important to understand what we mean by probability and to
understand a few basic rules for computing and manipulating probabilities. That is the pur-
pose of this chapter.
The material covered in this chapter has been selected for two reasons. First, it is di-
rectly applicable to an understanding of the material presented in the remainder of the
book. Second, it is intended to allow you to make simple calculations of probabilities that
are likely to be useful to you. Material that does not satisfy either of these qualifications
has been deliberately omitted. For example, we will not consider such things as the proba-
bility of drawing the queen of hearts, given that 14 cards, including the four of hearts, have
already been drawn. Nor will we consider the probability that your desk light will burn out
in the next 25 hours of use, given that it has already lasted 250 hours. The student who is
interested in those topics is encouraged to take a course in probability theory, in which such
material can be covered in depth.5.1 Probability
The concept of probability can be viewed in several different ways. There is not even gen-
eral agreement as to what we mean by the word probability. The oldest and perhaps the
most common definition of a probability is what is called the analytic view.One of the ex-
amples that is often drawn into discussions of probability is that of one of my favorite can-
dies, M&M’s. M&M’s are a good example because everyone is familiar with them, they
are easy to use in class demonstrations because they don’t get your hand all sticky, and you
can eat them when you’re done. The Mars Candy Company is so fond of having them used
as an example that they keep lists of the percentage of colors in each bag—though they
seem to keep moving the lists around, making it a challenge to find them on occasions.^1 At
present the data on the milk chocolate version is shown in Table 5.1.
Suppose that you have a bag of M&M’s in front of you and you reach in and pull one
out. Just to simplify what follows, assume that there are 100 M&M’s in the bag, though112 Chapter 5 Basic Concepts of Probability
(^1) Those instructors who have used several editions of this book will be pleased to see that the caramel example is
gone. I liked it, but other people got bored with it.
Table 5.1 Distribution of colors in an average bag of M&M’s
Color Percentage
Brown 13
Red 13
Yellow 14
Green 16
Orange 20
Blue 24
Total 100
analytic view