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7-5
7-5 Compound
CompoundEvents
Events
7-5 Compound Events
Objectives
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
Algebra 2Algebra 2
Holt
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
Find the probability of mutually
exclusive events.
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 dice
are mutually exclusive events.
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7-5 Compound Events
Remember!
Recall that the union symbol ∪ means “or.”
“or” means to add.
7-5 Compound Events
Example 1: 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.
means “and”
“and” means multiply
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.
What is the probability of having O or A type blood?
P(O U A) =9/20 + 2/5 = 17/20
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.
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7-5 Compound Events
7-5 Compound Events
Example 2: Finding Probabilities of Compound Events
Find the probability of rolling a 4 or an even
number on a number cube.
P(4 or even) = P(4) + P(even) – P(4 and even)
4 is also an even number.
“or” means to add.
When adding, don’t forget to subtract if they overlap!
X
Holt McDougal Algebra 2
Holt McDougal Algebra 2
7-5 Compound Events
Example 2B: Finding Probabilities of Compound
Events
Find the probability of rolling an odd number or a
number greater than 2
.
P(odd or >2) = P(odd) + P(>2) – P(odd and >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?
There are 2 outcomes where
the number is odd and
greater than 2.
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7-5 Compound Events
7-5 Compound Events
Example 3 Continued
Step 1 Use a Venn diagram.
Example 3 Continued
Step 2 Find the number in the overlapping region.
Label as much information as you know. Being a senior
and reading the paper are inclusive events.
Subtract 215 from 630. This is the number of senior
paper readers, 415.
Step 3 Find the probability.
1560
P(senior ∪ reads paper)
= P(senior) + P(reads paper) – P(senior ∩ reads paper)
840
630
Holt McDougal Algebra 2
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
7-5 Compound Events
Vocabulary
Example 3 Continued
simple event
describes a single outcome.
compound event
made up of two or more
simple events.
mutually exclusive events events that cannot
both occur in the same trial of an experiment.
inclusive events
Holt McDougal Algebra 2
events that have one or more
outcomes in common
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