Page 310 -

2. The observer may be interested not only in the elementary elements
occurrence, but in finding the probability of a certain event which
may consist of a set of elementary outcomes; for example:
a. An event may consist of “obtaining an even number of spots on
the upward face of a randomly rolled die.” This event then
consists of all successful trials having as experimental outcomes
any member of the set:

E = {, , }24 6 (10.4)

b. Another event may consist of “obtaining three or more spots”
(hence, we will use this form of abbreviated statement, and not
keep repeating: on the upward face of a randomly rolled die).
Then, this event consists of all successful trials having experi-
mental outcomes any member of the set:

B = {, , , }345 6 (10.5)

Note that, in general, events may have overlapping elementary
elements.

For a fair die, using the definition of the probability as the limit of a relative
frequency, it is possible to conclude, based on experimental trials, that:

PE() = P( ) +2 P( ) +4 P( ) =6 1 (10.6)
2
while

PB() = P( ) +3 P( ) +4 P( ) +5 P( ) =6 2 (10.7)
3
and

PS() = 1 (10.8)
The last equation [Eq. (10.8)] is the mathematical expression for the statement
that the probability of the event that includes all possible elementary out-
comes is 1 (i.e., certainty).
It should be noted that if we define the events O and C to mean the events
of “obtaining an odd number” and “obtaining a number smaller than 3,”
respectively, we can obtain these events’ probabilities by enumerating the
elements of the subsets of S that represent these events; namely:

PO() = P( ) +1 P( ) +3 P( ) =5 1 (10.9)
2

© 2001 by CRC Press LLC