Page 56 - Probability Demystified

CHAPTER 3 The Addition Rules 45

Addition Rule I

The probability of two or more events occurring can be determined by using
the addition rules. The first rule is used when the events are mutually
exclusive.

Addition Rule I: When two events are mutually exclusive,
PðA or BÞ¼ PðAÞþ PðBÞ

EXAMPLE: When a die is rolled, find the probability of getting a 2 or a 3.

SOLUTION:
As shown in Chapter 1, the problem can be solved by looking at the sample
space, which is 1, 2, 3, 4, 5, 6. Since there are 2 favorable outcomes from
2
1
6 outcomes, P(2 or 3) ¼ ¼ . Since the events are mutually exclusive,
6 3
addition rule 1 also can be used:
1 1 2 1
Pð2or3Þ¼ Pð2Þþ Pð3Þ¼ þ ¼ ¼
6 6 6 3

EXAMPLE: In a committee meeting, there were 5 freshmen, 6 sophomores,
3 juniors, and 2 seniors. If a student is selected at random to be the
chairperson, find the probability that the chairperson is a sophomore or a
junior.

SOLUTION:

There are 6 sophomores and 3 juniors and a total of 16 students.
6 3 9
P(sophomore or junior) ¼ PðsophomoreÞþ Pð juniorÞ¼ þ ¼
16 16 16

EXAMPLE: A card is selected at random from a deck. Find the probability
that the card is an ace or a king.

SOLUTION:
4 4 8 2
P(ace or king) ¼ PðaceÞþ PðkingÞ¼ þ ¼ ¼
52 52 52 13
The word or is the key word, and it means one event occurs or the other
event occurs.