7-5
7-5 Compound
CompoundEvents
Events
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
Algebra 2Algebra 2
Holt
7-5 Compound Events
Warm Up
One card is drawn from the deck. Find each
probability.
1. selecting a two
2. selecting a face card
Two cards are drawn from the deck. Find each
probability.
3. selecting two kings when the first card is
replaced.
4. selecting two hearts when the first card is not
replaced.
Holt McDougal Algebra 2
7-5 Compound Events
Objectives
Find the probability of mutually
exclusive events.
Find the probability of inclusive events.
Holt McDougal Algebra 2
7-5 Compound Events
Vocabulary
simple event
compound event
mutually exclusive events
inclusive events
Holt McDougal Algebra 2
7-5 Compound Events
A simple event is an event that describes a single
outcome. A compound event is an event made up of
two or more simple events. Mutually exclusive
events are events that cannot both occur in the same
trial of an experiment. Rolling a 1 and rolling a 2 on
the same roll of a number cube are mutually exclusive
events.
Holt McDougal Algebra 2
7-5 Compound Events
Remember!
Recall that the union symbol  means “or.”
Holt McDougal Algebra 2
7-5 Compound Events
Example 1A: Finding Probabilities of Mutually
Exclusive Events
A group of students is donating blood during a
blood drive. A student has a
having type O blood and a
probability of
probability of
having type A blood.
Explain why the events “type O” and “type A”
blood are mutually exclusive.
A person can only have one blood type.
Holt McDougal Algebra 2
7-5 Compound Events
Example 1B: Finding Probabilities of Mutually
Exclusive Events
A group of students is donating blood during a
blood drive. A student has a
having type O blood and a
probability of
probability of
having type A blood.
What is the probability that a student has type O
or type A blood?
P(type O  type A) = P(type O) + P(type A)
Holt McDougal Algebra 2
7-5 Compound Events
Check It Out! Example 1a
Each student cast one vote for senior class
president. Of the students, 25% voted for Hunt,
20% for Kline, and 55% for Vila. A student from
the senior class is selected at random.
Explain why the events “voted for Hunt,” “voted
for Kline,” and “voted for Vila” are mutually
exclusive.
Each student can vote only once.
Holt McDougal Algebra 2
7-5 Compound Events
Check It Out! Example 1b
Each student cast one vote for senior class
president. Of the students, 25% voted for Hunt,
20% for Kline, and 55% for Vila. A student from
the senior class is selected at random.
What is the probability that a student voted for
Kline or Vila?
P(Kline  Vila) = P(Kline) + P(Vila)
= 20% + 55% = 75%
Holt McDougal Algebra 2
7-5 Compound Events
Inclusive events are events that have one or more
outcomes in common. When you roll a number cube,
the outcomes “rolling an even number” and “rolling a
prime number” are not mutually exclusive. The number
2 is both prime and even, so the events are inclusive.
Holt McDougal Algebra 2
7-5 Compound Events
There are 3 ways to roll an even number, {2, 4, 6}.
There are 3 ways to roll a prime number, {2, 3, 5}.
The outcome “2” is counted twice when outcomes are
added (3 + 3) . The actual number of ways to roll an
even number or a prime is 3 + 3 – 1 = 5. The concept
of subtracting the outcomes that are counted twice
leads to the following probability formula.
Holt McDougal Algebra 2
7-5 Compound Events
Holt McDougal Algebra 2
7-5 Compound Events
Remember!
Recall that the intersection symbol  means
“and.”
Holt McDougal Algebra 2
7-5 Compound Events
Example 2A: Finding Probabilities of Compound
Events
Find the probability on a number cube.
rolling a 4 or an even number
P(4 or even) = P(4) + P(even) – P(4 and even)
4 is also an even number.
Holt McDougal Algebra 2
7-5 Compound Events
Example 2B: Finding Probabilities of Compound
Events
Find the probability on a number cube.
rolling an odd number or a number greater than 2
P(odd or >2) = P(odd) + P(>2) – P(odd and >2)
There are 2 outcomes where
the number is odd and
greater than 2.
Holt McDougal Algebra 2
7-5 Compound Events
Check It Out! Example 2a
A card is drawn from a deck of 52. Find the
probability of each.
drawing a king or a heart
P(king or heart) = P(king) + P(heart) – P(king and heart)
Holt McDougal Algebra 2
7-5 Compound Events
Check It Out! Example 2b
A card is drawn from a deck of 52. Find the
probability of each.
drawing a red card (hearts or diamonds) or a
face card (jack, queen, or king)
P(red or face) = P(red) + P(face) – P(red and face)
Holt McDougal Algebra 2
7-5 Compound Events
Example 3: Application
Of 1560 students surveyed, 840 were seniors and
630 read a daily paper. The rest of the students
were juniors. Only 215 of the paper readers were
juniors. What is the probability that a student
was a senior or read a daily paper?
Holt McDougal Algebra 2
7-5 Compound Events
Example 3 Continued
Step 1 Use a Venn diagram.
Label as much information as you know. Being a
senior and reading the paper are inclusive events.
Holt McDougal Algebra 2
7-5 Compound Events
Example 3 Continued
Step 2 Find the number in the overlapping region.
Subtract 215 from 630. This is the number of senior
paper readers, 415.
Step 3 Find the probability.
P(senior  reads paper)
= P(senior) + P(reads paper) – P(senior  reads paper)
The probability that the student was a senior or read
the daily paper is about 67.6%.
Holt McDougal Algebra 2
7-5 Compound Events
Example 3 Continued
Holt McDougal Algebra 2
7-5 Compound Events
Check It Out! Example 3
Of 160 beauty spa customers, 96 had a hair
styling and 61 had a manicure. There were 28
customers who had only a manicure. What is the
probability that a customer had a hair styling or
a manicure?
Holt McDougal Algebra 2
7-5 Compound Events
Check It Out! Example 3 Continued
Step 1 Use a Venn diagram.
Label as much information as you know. Having a hair
styling and a manicure are inclusive events.
160 customers
63 33 28
hair styling
Holt McDougal Algebra 2
manicure
7-5 Compound Events
Check It Out! Example 3 Continued
Step 2 Find the number in the overlapping region.
Subtract 28 from 61. This is the number of hair
stylings and manicures, 33.
Step 3 Find the probability.
P(hair  manicure) =
P(hair) + P(manicure) – P(hair  manicure)
The probability that a customer had a hair styling or
manicure is 77.5%.
Holt McDougal Algebra 2
7-5 Compound Events
Recall from Lesson 11-2 that the complement of an
event with probability p, all outcomes that are not in
the event, has a probability of 1 – p. You can use the
complement to find the probability of a compound
event.
Holt McDougal Algebra 2
7-5 Compound Events
Example 4 Application
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability
that at least 2 students choose the same
butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
Use the complement.
Holt McDougal Algebra 2
7-5 Compound Events
Example 4 Continued
P(at least 2 students choose same) = 1 – 0.0769 ≈ 0.9231
The probability that at least 2 students choose the
same butterfly is about 0.9231, or 92.31%.
Holt McDougal Algebra 2
7-5 Compound Events
Check It Out! Example 4
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
P(two customers bought same earrings) =
1 – P(all choose different)
Use the complement.
Holt McDougal Algebra 2
7-5 Compound Events
Check It Out! Example 4 Continued
P(at least 2 choose the same)  1 – 0.8476  0.1524
The probability that at least 2 customers buy the
same style is about 0.1524, or 15.24%.
Holt McDougal Algebra 2
7-5 Compound Events
Lesson Quiz: Part I
You have a deck of 52 cards.
1. Explain why the events “choosing a club” and
“choosing a heart” are mutually exclusive.
A card can have only one suit.
2. What is the probability of choosing a club or a
heart?
Holt McDougal Algebra 2
7-5 Compound Events
Lesson Quiz: Part II
The numbers 1–9 are written on cards and
placed in a bag. Find each probability.
3. choosing a multiple of 3 or an even number
4. choosing a multiple of 4 or an even number
5. Of 570 people, 365 were male and 368 had
brown hair. Of those with brown hair, 108 were
female. What is the probability that a person
was male or had brown hair?
Holt McDougal Algebra 2
7-5 Compound Events
Lesson Quiz: Part III
6. Each of 4 students randomly chooses a pen
from 9 styles. What is the probability that at
least 2 students choose the same style?
 0.5391
Holt McDougal Algebra 2