Page 60 - Probability Demystified

CHAPTER 3 The Addition Rules 49

EXAMPLE: At a political rally, there are 8 Democrats and 10 Republicans.
Six of the Democrats are females and 5 of the Republicans are females. If a
person is selected at random, find the probability that the person is a female
or a Democrat.

SOLUTION:
There are 18 people at the rally. Let PðfemaleÞ¼ 6 þ 5 ¼ 11 since there are
18
18
8
11 females, and PðDemocratÞ¼ 18 since there are 8 Democrats. Pðfemale and
DemocratÞ¼ 6 since 6 of the Democrats are females. Hence,
18
Pðfemale or DemocratÞ¼ PðfemaleÞþ PðDemocratÞ
Pðfemale and DemocratÞ
11 8 6 13
¼ þ ¼
18 18 18 18

EXAMPLE: The probability that a student owns a computer is 0.92, and
the probability that a student owns an automobile is 0.53. If the probability
that a student owns both a computer and an automobile is 0.49, find
the probability that the student owns a computer or an automobile.

SOLUTION:

Since P(computer) ¼ 0.92, P(automobile) ¼ 0.53, and P(computer and auto-
mobile) ¼ 0.49, P(computer or automobile) ¼ 0.92 þ 0.53 0.49 ¼ 0.96.
The key word for addition is ‘‘or,’’ and it means that one event or the other
occurs. If the events are not mutually exclusive, the probability of the
outcomes that the two events have in common must be subtracted from the
sum of the probabilities of the two events. For the mathematical purist, only
one addition rule is necessary, and that is

PðA or BÞ¼ PðAÞþ PðBÞ PðA and BÞ
The reason is that when the events are mutually exclusive, P(A and B)
is equal to zero because mutually exclusive events have no outcomes in
common.