Unit #10: Probability & Statistics
Lesson #2:
Sets and
Probability
Sets
• A set is a collection of unique elements.
• A roster is a list of elements in a set,
separated by commas surrounded by
“curly brackets”.
• Example: A = {1, 2, 3, 4, 5}
B = {May, June, July}
• The empty set is denoted with the
symbols ∅or
.
Lesson #2: Sets and Probability
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Unit #10: Probability & Statistics
Sets and Notation
Let set A be the numbers 3, 6, 9.
Write set A in roster notation.
3, 6, 9
Notation: 3 is an element of set A
3∈
Notation: 5 is not an element of set A
5∈
Sets
• A subset is any set whose elements are
from the original set, but does not include
all elements from the original set.
Given:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Set B contains all even integers from Set A.
Set C contains all integers greater than 6 that
are from Set A.
(a) Write sets B and C in roster notation.
2, 4, 6, 8, 10
7, 8, 9, 10
Lesson #2: Sets and Probability
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Unit #10: Probability & Statistics
Sets
Given:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Set B contains all even integers from Set A.
Set C contains all integers greater than 6 that are
from Set A.
(b) Do sets B and C have any elements in common?
Yes.
8, 10
Intersection of Sets B and C:
∩
Elements that are COMMON to both sets
Sets
Given:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Set B contains all even integers from Set A.
Set C contains all integers greater than 6 that are
from Set A.
(c) If you combine sets B and C, what would the
new set look like?
2, 4, 6, 7, 8, 9, 10
Union of Sets B and C:
∪
ALL elements in BOTH sets
Lesson #2: Sets and Probability
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Unit #10: Probability & Statistics
Sets
Given:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Set B contains all even integers from Set A.
Set C contains all integers greater than 6 that are
from Set A.
(d) What elements are in set A, but not in set C?
1, 2, 3, 4, 5, 6
Complement of Set C: ′
Elements that are not in the given set
Sets and Venn Diagrams
Sets are often represented in pictorial form with
a circle containing the elements of the set which
are called Venn Diagrams.
Lesson #2: Sets and Probability
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Unit #10: Probability & Statistics
Example 1: Given sets A, B, and C below. Find the following:
(a)
∩
4, 7
(b)
∪
1, 2, 8, 4, 7, 12, 44
(c)
∪
1, 2, 8, 4, 7, 17, 41
(d)
∩
or ∅
Example 2: In a class of 50 students, 18 take Chorus,
26 take Band, and 2 take both Chorus and Band. How
many students in the class are not enrolled in either
Chorus or Band?
50studentstotal
studentsinchorus
studentsleft
studentsinband
studentsleft
studentsinbandANDchorus
students
notenrolledineither
chorusorband
Lesson #2: Sets and Probability
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Unit #10: Probability & Statistics
Example 3: A single card is randomly selected from a
standard deck of 52 cards. Find the probability that
the selected card is:
(a) an ace or a king
(b) a red card or black card
(c) a black card or 10 of diamonds
(b)
(a)
(c)
or
or
*certain event!
Example 4:WVHS statistics students surveyed 52
seniors about their plans after high school and the data
is presented in the table below.
Male (M)
Female (F)
Total
Going to College (C)
16
13
29
Not Going to
College (N)
14
9
23
Total
30
22
52
Find the following probabilities if one student is selected
at random from the sample:
(a) P(M)
Lesson #2: Sets and Probability
(b) P(M and C)
(c) P(F or C)
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Unit #10: Probability & Statistics
Example 5: A standard 6-sided die is rolled once.
(a) Draw a Venn diagram to illustrate the probability that
the number rolled was either an even number or a
multiple of 3.
(b) Find the probability that the number rolled was either
an even number or a multiple of 3.
, , , , ,
(b)
Example 6: The Venn Diagram below represents the
sports played by 9th grade male students.
If a student is selected at
random, find:
(a) P(plays basketball)
(b) P(plays bball or football)
(c) P(plays bball and football)
(d) P(does not play bball or fball)
Lesson #2: Sets and Probability
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