The document discusses probability rules for compound events, noting that the multiplication rule is used to find the probability of two events happening together, while the addition rules are used to find the probability of one event or another occurring. It explains that the addition rule for mutually exclusive events is that the probability of event A or B is equal to the probability of A plus the probability of B, while the general addition rule for any events is the probability of A or B is equal to the probability of A plus the probability of B minus the probability of A and B occurring together.

1. 4.2 SOME PROBABILITY RULES –
COMPOUND EVENTS
PART 2: ADDITION RULES
Chapter 4: Elementary Probability Theory

2. Page
147
Multiplication VS Addition
 Multiplication  Addition Rules are
Rules are used to used to find the
find the probability probability of one
of two events event or another
Notice the
happening occurring. condition A or B
together. is satisfied by
any of the
following:
1. Any outcome
in A occurs
2. Any outcome
in B occurs
The Event A and B The Event A or B 3. Any outcome
Figure 4-4(a) Figure 4-4 (b) in both A and
B occurs

3. Page
Example – Combining Events 148
 Indicate how each of the following pairs of
events are combined. Use either the and
combination or the or combination.
a) Satisfying the humanities requirement by taking
a course in the history of Japan or by taking a
course in classical literature.
b) Buying new tires and aligning the tires.
c) Getting an A not only in psychology but also in
biology.
d) Having at least one of these pets:
cat, dog, bird, rabbit.

4. Be Careful! Page
Do Not confuse 149
Addition Rules “independence” with
“mutually exclusive”
 Two events are mutually exclusive or
disjoint if they cannot occur together. In
particular, events A and B are mutually
exclusive if P(A and B) = 0.
 Addition Rule for Mutually Exclusive
EventsThe addition rule for mutually exclusive
P(Aevents can be expandedP(B) adding!
or B) exclusive events… keep than two
mutually
= P(A) + for more
(page 151)
 General Addition Rule for ANY Events

5. Page
150
How to Use the Addition Rules
1. Determine whether A and B are mutually
exclusive events.
If P(A and B) = 0, then the events are mutually
exclusive
2. If A and B are mutually exclusive events
P(A or B) = P(A) + P(B)
3. If A and B are not mutually exclusive events
P(A or B) = P(A) + P(B) – P(A and B)

6. Page
Example 6 – Probability of Events 148
Combined with OR
 Consider an introductory statistics class with
31 students. The students range from
freshmen through seniors. Some students are
male and some are female. Figure 4-5 shows
the sample space. a) Suppose we select one
student at random from the
class. Find the probability
that the student is either a
freshman or a sophomore.
b) Select one student at
random from the class.
What is the probability that
the student is either a male
Sample Space for Statistics Class
or a sophomore?
Figure 4-5

7. Page
Example 7 – Mutually Exclusive 151
Events
 Laura is playing Monopoly. On her next move
she needs to throw a sum bigger than 8 on the
two dice in order to land on her own property
and pass Go. What is the probability that
Laura will roll a sum bigger than 8?

8. Solution – Mutually Exclusive
Events
When two dice are thrown, the
largest sum that can come up is
12. Consequently, the only sums
larger than 8 are 9, 10, 11, and
12. These outcomes are mutually
exclusive, since only one of
these sums can possibly occur
on one throw of the dice.
P(9 or 10 or 11 or 12) = P(9) + P(10) + P(11) + P(12)

9. Page
Summary of Basic Probability 154
Rules
 Use this chart!!
 Also See Table 4-3 “English Phrases and
Corresponding Symbolic Translations”

10. Assignment
 Page 155
 #1, 3, 4, 7, 11, 13, 17, 23, 27f