CCGPS Geometry
Unit 6 – Probability
6-1 Notes
Name: _______________________________________ Date: _______________________
Vocabulary, Set Notation, & Venn Diagrams
Probability
 . A number from 0 to 1

As a percent from ________ to __________

Indicates how likely an ________________will
occur.
#
#
Experiment
 Any process or action that has observable results

Example: ____________________________________________________________________
Outcomes
 _______________________________________________________________________________

Example: _____________________________________________________________________
Sample Space
 The set (or list) of ______________________________________________________________

Also known as the ___________________________________________________________

Example: ____________________________________________________________________
Event
 A subset of an ______________________________________________________________

An outcome or _____________________________________________________________

Example: ____________________________________________________________________

_______________________________________________________________________________
Set
Subset
 List or collection of ____________ all contained within another set.

Denoted by ____________________ if all the elements of A are also in B.
CCGPS Geometry
Unit 6 – Probability
6-1 Notes
Empty Set
 A set that has ________ _____________________________

Also called a __________ _____________

Denoted by _____________
Union
 Denoted by ___________

To unite

Everything in ________ sets
Intersection
 Denoted by ___________

Only what the sets _____________ in common.
Complement
 Denoted two different ways: ____________ or ____________

Everything _______________ of this set
Hector has entered the following names in the contact list of his new cellphone: Alicia,
Brisa, Steve, Don, and Ellis.
B: The name starts with a vowel
1. Draw a venn diagram to represent this.
2. List the outcomes of B.
3. List the outcomes of E.
4. List the outcomes of BE.
5. List the outcomes of BE.
6. List the outcomes of B’.
7. List the outcomes of (BE)’.
E: The name ends in a vowel.
Set Notation
A B
A B
A or A '
 A  B '
 A  B '
Pronunciation
“A union B”
“A intersect B”
Meaning
Everything in
Venn Diagram
A
B
both sets
Only what is in
common with
A
B
both sets
“A complement”
“not A union B”
“ not A intersect B”
Everything NOT
A
B
in set A
Everything NOT in
A
B
set A or set B
Everything NOT in
common between
set A and set B
A
B
Answer
CCGPS Geometry
Unit 6 – Probability
6-1 CW
Using Venn Diagrams
Shade in the appropriate area of the Venn Diagram.
1. A  B
A
2. A  B '
B
4. B  C
A
5. A  B  C
Mr. Grisham took a poll of his student’s favorite type
of weather. The students had the choice of hot, cold,
and/or rain/snow. The results are displayed in the
Venn Diagram. Write your answer as a reduced fraction
6. Find P(Cold).
7. Find P(Warm)’.
8. Find P(Cold Warm).
9. Find P(Warm  Rain).
10. Find P(Warm  Cold  Rain).
11. Find P(Cold  Warm).
3. A '
B
A
6. A  B '
B
SETS
Section 6-1
1.
A. Make a VENN diagram of the following Chart showing
what classes each student was enrolled in this semester.
Name
Math
Language Arts
Science


Ashley


Betsy



Chris


Devonte


Eder
Frank

George

Heather

Isabella

Jessica

Krista
Name:
Science
B. (𝑳𝑨):
2.
LA
Math
C. (𝑴𝒂𝒕𝒉 ∩ 𝑺𝒄𝒊𝒆𝒏𝒄𝒆):
D. (𝑴𝒂𝒕𝒉)′:
E. (𝑴𝒂𝒕𝒉 ∪ 𝑳𝑨):
F. (𝑴𝒂𝒕𝒉 ∪ 𝑳𝑨)′:
G. (𝑴𝒂𝒕𝒉 ∩ 𝑳𝑨′):
H. (𝑴𝒂𝒕𝒉 ∩ 𝑳𝑨 ∩ 𝑺𝒄𝒊𝒆𝒏𝒄𝒆):
I. (𝑴𝒂𝒕𝒉 ∪ 𝑳𝑨) ∩ (𝑺𝒄𝒊𝒆𝒏𝒄𝒆):
J. (𝑴𝒂𝒕𝒉 ∩ 𝑳𝑨) ∪ (𝑺𝒄𝒊𝒆𝒏𝒄𝒆):
Given
A = { 1, 2, 3, 6, 7, 9}
, B = { 2, 4, 6, 7, 8} ,
and
U = { 1, 2, 3, 4, 5, 6, 7, 8, 9}
A. (𝑨 ∩ 𝑩):
B. (𝑨 ∪ 𝑩):
C. (𝑨)′:
D. (𝑨 ∩ 𝑩)′:
M. Winking (Section 7-1)
answer the following.
p. 149
3.
A manager that owns 3 local area Car Maintenance Garages was researching certifications of mechanics that worked for her
company. Consider the following Venn diagram.
a.
How many mechanics worked for her company?
ASE Certified
ASE Certified
b.
c.
How many of the mechanics are certified by ASE to
do work on Brakes?
A/C Repair
1
Brakes
4
3
2
2
How many of the mechanics are certified by ASE to do work
on Brakes and Tune-Ups (Brakes  Tune-Ups)?
0
3
d.
e.
4.
How many of the mechanics are certified by ASE to do work
on either A/C or Tune-Ups (A/C  Tune-Ups)??
3
ASE Certified
Not ASE
Engine Tune-Ups
Certified
How many of the mechanics have their certification in Brakes or A/C but not in Tune-Ups???
(𝐵𝑟𝑎𝑘𝑒𝑠 ∪ 𝐴/𝐶) ∩ (𝑇𝑢𝑛𝑒 𝑈𝑝𝑠)’
The following Venn diagram shows a breakdown of a small high schools sports program.
a. How many students play only Tennis?
b.
How many students play basketball and tennis?
Play
Play Baseball
c.
d.
How many students play basketball or softball/baseball?
𝐵𝑎𝑠𝑘𝑒𝑡𝑏𝑎𝑙𝑙 ∪ 𝐵𝑎𝑠𝑒𝑏𝑎𝑙𝑙/𝑆𝑜𝑓𝑡𝑏𝑎𝑙𝑙
or Softball
12
How many students play baseball/softball or tennis but not
basketball?
(𝐵𝑎𝑠𝑒𝑏𝑎𝑙𝑙/𝑆𝑜𝑓𝑡𝑏𝑎𝑙𝑙 ∪ 𝑇𝑒𝑛𝑛𝑖𝑠) ∩ (𝐵𝑎𝑠𝑘𝑒𝑡𝑏𝑎𝑙𝑙)′
8
How many students that play a sport do not play basketball?
f.
How many students attend this school?
g.
How many students do not play tennis in total?
M. Winking (Section 7-1)
20
3
2
2
14
Play
e.
Basketball
Tennis
552
Do not
play one of
these sports
p. 150
5.
In the state of Oregon, all of the area codes start with a number greater than 4 and end in an odd number
(e.g. 503-232-1235, 971-923-5648). Let A represent the set of all area codes that start with an even number.
Let B represent the set of all area codes that could be used in Oregon by the requirements stated earlier.
Which might be an area code that belongs to the set (𝑨 ∩ 𝑩)?
A. 403
B. 792
C. 892
D. 631
Which might be an area code that belongs to the set (𝑨 ∩ 𝑩′)?
A. 403
B. 792
C. 892
D. 631
Which might be an area code that belongs to the set (𝑨′ ∩ 𝑩′)?
A. 403
6.
B. 792
C. 892
D. 631
In a particular state, the first character on a license plate is always a letter. The last character is always a digit
from 0 to 9. Let V represents the set of all license plates beginning with a vowel, and O represents the set of all
license plates that end with an odd number,
Which might be a license plate that belongs to the set (𝑽 ∩ 𝑶)?
A.
B.
C.
D.
C.
D.
C.
D.
Which might be a license plate that belongs to the set (𝑽 ∩ 𝑶′)?
A.
B.
Which might be a license plate that belongs to the set (𝑽′ ∩ 𝑶′)?
A.
B.
M. Winking (Section 7-1)
p. 151
Extra Copies To Mark On While Solving Problems
LA
Math
Devonte
Devonte
Heather
Jessica
Isabella
Krista
Chris
Ashley
Eder
Betsy
Frank
George
Devonte
Heather
Jessica
Isabella
Krista
Chris
Ashley
Eder
Betsy
Frank
George
Frank
Science
LA
LA
Math
Devonte
Devonte
Heather
Jessica
Heather
Jessica
Isabella
Krista
Chris
Chris
Ashley
Eder
Betsy
George
Betsy
George
Science
Ashley
Eder
Heather
Jessica
Isabella
Krista
Chris
Isabella
Krista
LA
Math
Devonte
Math
Frank
Science
LA
Ashley
Eder
Betsy
George
Science
Math
Heather
Jessica
Isabella
Krista
Chris
Ashley
Eder
LA
Math
Frank
Betsy
George
Frank
Science
Science
M. Winking (Section 7-1)
p. 152