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A Venn Diagram is made up of two or more circles. It is often used in organized counting to
show relationships between events
Rectangle ‘S’ represents a s’ample space of possible outcomes.
Circles ‘A’ and ‘B’ each represent specific unique events in the sample space S
If it is possible lbr two events A and B to both happen at the same time, then their circles will
intersect on a Venn Diagram.
a.
I. Shade the region of the picture corresponding to each listed event.
1.)A
2.) 13
3.) AnB
4.)AuB
The complement ofan event ‘A’ refers to all outcomes that are NOT included in ‘A’.
The notation for complement is A’
Shade the region corresponding to each listed event.
6.) B’
5.) A’
4
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7.) (A
n
8.)
B)’
(Au B)’
/
Complete #9-13 on a separate sheet of paper. Let ‘S’ represent rolling a 6-sided die. A and
B represent different events. Draw Venn diagrams for each pair of events below.
9.)
11
.)
A = number less than 3
B = an even number
10.)
A = a ‘2’
B = a ‘3’
12.)
13.) In which problem (#9
—
A
B
=
=
a
an even number
A = a# greater than or equal to ‘1’
B = a # less than or equal to ‘6’
12) are the events mutually exclusive?
II. 80 students were asked if they take Math and History classes. The Venn diagram shows
the number of students who took each class. Suppose one student is chosen at random, and
incivur ihi’ n;iptinn’.i holnw
Students in History
Students in Math
17
13.) n(studenis taking Math)
=
14.) n(students taking History)
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3]
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LID
=
15.) n(students taking Math AND History)
16.) n(students taking Math OR History)
=
=
UI
22 +
17.) What does the ‘17’ represent in the diagram above?
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IJI. Students’ records indicate that the percentage of students passing photography is
75%, the number of students failing economics is 65%, and the number of students passing
at least one of the two courses is 85%. Regions A, B, C, and 1) make up the entire sample
space of students taking both classes.
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b= ;o
A
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Passing Economies
Passing Photography
19.) Which regions (A.B.c. or D) represent passing both classes?
20.) Which regions represent failing both classes?
A
21.) Which regions represent passing exactly one class?
22.) n(passing
economics)
24
=
23.) n(passing both courses)
24.) n(fttiling both courses)
=
=
K
A
25.) n(passing exactly one course)
=
z
‘Eo
(0
C
IV. 106 women who recently gave birth were given a survey with 3 yes/no questions, and
the following information was recorded.
The mother...
Is over 35 years_of age
Just had her first child
I las a career
Is over 35 and just had First_child
Ilas a career and just had first child
Is over 35 and has a career
Is over 35, has a career, and just had first child
—
-_____
—
LP!{espondents
27
2!
42
17
H
16
H
Use the Venn Diagram to organize the information.
If a mother from this group is randomly selected, tind the probabilities below.
26.) n(replied ‘yes’ to exactly 2 of the 3 questions above)
t 04—
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t
27.) n(replied ‘yes’ to at least 2 of the 3 questions above)
Li-
28.) n(replied yes’ to at least one of the 3 questions above)
29.) n(replied ‘yes’ to none of the 3 questions above)
—
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