Chapter 7 Sets & Probability Section 7.2 Applications of

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Chapter 7Sets Probability

• Section 7.2
• Applications of Venn Diagrams

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Shade the region corresponding to A ? ? B .
A
B
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Shade the region corresponding to A ? ? B .
Step 1 Shade the region corresponding to A ?.
A
B
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Shade the region corresponding to A ? ? B .
Step 2 Shade the region corresponding to B .
A
B
The intersection of A ? ? B is the overlapping
region that has been shaded twice.
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Shade the region corresponding to A ? ? B .
A ? ? B
A
B
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• Use a Venn diagram to shade in the region
  corresponding to the indicated set.
• a.) B ? A?
• b.) B ? ? (A? ? C ?)
• c.) A ? (B ? C) ?

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• A survey of 200 people yielded the following
  information 94 owned a VCR, 127 owned a
  microwave oven, and 78 owned both. How many
  people owned the following?
• a.) a VCR or a microwave oven
• b.) a VCR but not a microwave
• c.) a microwave oven but not a VCR
• d.) neither a VCR nor a microwave oven

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• A survey of 200 people yielded the following
  information 94 owned a VCR, 127 owned a
  microwave oven, and 78 owned both.
• n(U) 200
• n(V) 94
• n(M) 127
• n(V ? M) 78

V
M
49
78
16
57
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• A survey of 200 people yielded the following
  information 94 owned a VCR, 127 owned a
  microwave oven, and 78 owned both. How many
  people owned

a.) a VCR or microwave oven? n (V ? M)
16 78 49 143 b.) a VCR, but not a
microwave oven? n (V ? M?) 16 c.) a
microwave oven, but not a VCR? n (M ? V?)
49 d.) neither a VCR nor a microwave oven?
n (M? ? V?) 57
V
M
49
78
16
57
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• The records of 1492 high school graduates were
  examined, and the following information was
  obtained 1072 took biology, and 679 took
  geometry. If 271 of those who took geometry did
  not take biology, how many graduates took the
  following?
• a.) both classes
• b.) at least one of the classes
• c.) biology but not geometry
• d.) neither class

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In a survey, 674 adults were asked what
television programs they had recently watched.
The following information was obtained 226
watched neither the Big Game nor the New Movie,
and 289 watched the New Movie. If 183 of those
who watched the New Movie did not watch the Big
Game, how many of the surveyed adults watched the
following? a.) both programs b.) at least one
program c.) the Big Game d.) the Big Game but
not the New Movie
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Recently, U2, Sting, and Lollapalooza each toured
the United States. A large group of college
students was surveyed, and the following
information was obtained 1533 saw U2, 1127 saw
Sting, 581 saw Lollapalooza, 219 saw all three,
1853 saw none, 766 saw only U2, 654 saw U2 and
Sting, and 92 saw Sting and Lollapalooza but not
U2. a.) What percent of the college students
saw all three acts? b.) What percent of the
college students saw at least two of the acts?
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• A kindergarten teacher wants to do an activity
  about common household pets. She begins the
  activity by asking her class the following
  questions and records the childrens answers.
• How many of you have a dog? 15
• How many of you have a cat? 10
• How many of you have both? 7
• How many of the children had a dog or a cat?

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Union Rule for Sets (General Rule)

• n(A ? B) n(A) n(B) n(A ? B)
• n(D) 15 n(C) 10 n(D ? C) 7
• n(D ? C) n(D) n(C) n(D ? C)
• n(D ? C) 15 10 7
• n(D ? C) 18

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Union Rule for Disjoint Sets

• n(A ? B) n(A) n(B)
• Note Use this rule only when the two sets do
• not have any elements in common.
• To be on the safe side, you can always use the
  General Union Rule for Sets.

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A company that specializes in language tutoring
lists the following information concerning its
English-speaking employees 23 speak German, 25
speak French, 31 speak Spanish, 43 speak Spanish
or French, 38 speak French or German, 46 speak
German or Spanish, 8 speak Spanish, French, and
German, and 7 office workers and secretaries
speak English only. a.) What percent of the
employees speak at least one language
other than English? b.) What percent of the
employees speak at least two languages
other than English?