Page 14 - Probability Demystified

CHAPTER 1 Basic Concepts 3

outcomes of the sample space. (Note: It is sometimes necessary to consider
an event which has no outcomes. This will be explained later.)
An event with one outcome is called a simple event. For example, a die is
rolled and the event of getting a four is a simple event since there is only one
way to get a four. When an event consists of two or more outcomes, it is
called a compound event. For example, if a die is rolled and the event is getting
an odd number, the event is a compound event since there are three ways to
get an odd number, namely, 1, 3, or 5.
Simple and compound events should not be confused with the number of
times the experiment is repeated. For example, if two coins are tossed, the
event of getting two heads is a simple event since there is only one way to get
two heads, whereas the event of getting a head and a tail in either order is
a compound event since it consists of two outcomes, namely head, tail and
tail, head.

EXAMPLE: A single die is rolled. List the outcomes in each event:
a. Getting an odd number

b. Getting a number greater than four
c. Getting less than one

SOLUTION:
a. The event contains the outcomes 1, 3, and 5.
b. The event contains the outcomes 5 and 6.

c. When you roll a die, you cannot get a number less than one; hence,
the event contains no outcomes.

Classical Probability

Sample spaces are used in classical probability to determine the numerical
probability that an event will occur. The formula for determining the
probability of an event E is

number of outcomes contained in the event E
PðEÞ¼
total number of outcomes in the sample space