Page 43 - Probability Demystified

32 CHAPTER 2 Sample Spaces

Notice that the sample space consists of ordered pairs of numbers. The
outcome (4, 2) means that a 4 was obtained on the first die and a 2 was
obtained on the second die. The sum of the spots on the faces in this case is
4 þ 2 ¼ 6. Probability problems involving rolling two dice can be solved using
the sample space shown in Figure 2-11.

EXAMPLE: When two dice are rolled, find the probability of getting a sum
of nine.

SOLUTION:
There are four ways of rolling a nine. They are (6, 3), (5, 4), (4, 5), and (3, 6).
The sample space consists of 36 outcomes. Hence,

4 1
Pð9Þ¼ ¼
36 9

EXAMPLE: When two dice are rolled, find the probability of getting
doubles.

SOLUTION:
There are six ways to get doubles. They are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5),
and (6, 6); hence
6 1
PðdoublesÞ¼ ¼
36 6

EXAMPLE: When two dice are rolled, find the probability of getting a sum
less than five.

SOLUTION:
A sum less than five means a sum of four, three, or two. There are three ways
of getting a sum of four. They are (3, 1), (2, 2), and (1, 3). There are two ways
of getting a sum of three. They are (2, 1), and (1, 2). There is one way of
getting a sum of two. It is (1, 1). The total number of ways of getting a sum
less than five is 3 þ 2 þ 1 ¼ 6. Hence,
6 1
P(sum less than 6) ¼ ¼
36 6