College Algebra

Michael Sullivan

Chapter 10

Counting and Probability

Educators


Problem 1

The ____ of $A$ and $B$ consists of all elements in either $A$ or $B$ or both.

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Problem 2

The ___ of $A$ with $B$ consists of all elements in both $A$ and $B .

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Problem 3

The intersection of two sets is always a subset of their union.

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Problem 4

If $A$ is a set, the complement of $A$ is the set of all the elements in the universal set that are not in $A$.

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Problem 5

If each element of a set $A$ is also an element of a set $B,$ we say that $A$ is a ___
of $B$ and write $A$ ___$B$.

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Problem 6

If the number of elements in a set is a non negative integer, we say that the set is ____.

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Problem 7

If $A$ and $B$ are finite sets, the Counting Formula states that $n(A \cup B)=$ ____

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Problem 8

If a task consists of a sequence of three choices in which there are $p$ selections for the first choice, $q$ selections for the second choice, and $r$ selections for the third choice, the task of making these selections can be done in $p \cdot q \cdot r$ different ways.

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Problem 9

Write down all the subsets of $\{a, b, c, d\}$.

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Problem 10

Write down all the subsets of $\{a, b, c, d, e\}$.

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Problem 11

\begin{aligned}
&\text { If } n(A)=15, n(B)=20, \text { and } n(A \cap B)=10\\
&\text { find } n(A \cup B)
\end{aligned}.

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Problem 12

\begin{aligned}
&\text { If } n(A)=30, n(B)=40, \text { and } n(A \cup B)=45\\
&\text { find } n(A \cap B)
\end{aligned}

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Problem 13

\begin{aligned}
&\text { If } n(A \cup B)=50, n(A \cap B)=10, \text { and } n(B)=20, \text { find }\\
&n(A)
\end{aligned}

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Problem 14

If $n(A \cup B)=60, n(A \cap B)=40,$ and $n(A)=n(B),$ find $n(A)$

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Problem 15

Use the information given in the figure.
(FIGURE CANNOT COPY)
How many are in set $A$ ?

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Problem 16

Use the information given in the figure.
(FIGURE CANNOT COPY)
How many are in set $B ?$

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Problem 17

Use the information given in the figure.
(FIGURE CANNOT COPY)
How many are in $A$ or $B ?$

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Problem 18

Use the information given in the figure.
(FIGURE CANNOT COPY)
How many are in $A$ and $B ?$

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Problem 19

Use the information given in the figure.
(FIGURE CANNOT COPY)
How many are in $A$ but not $C$ ?$

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Problem 20

Use the information given in the figure.
(FIGURE CANNOT COPY)
How many are not in $A$ ?

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Problem 21

Use the information given in the figure.
(FIGURE CANNOT COPY)
How many are in $A$ and $B$ and $C ?$

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Problem 22

Use the information given in the figure.
(FIGURE CANNOT COPY)
How many are in $A$ or $B$ or $C ?$

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Problem 23

A man has 5 shirts and 3 ties. How many different shirt and tie arrangements can he wear?

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Problem 24

$A$ woman has 5 blouses and 8 skirts. How many different outfits can she wear?

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Problem 25

How many four-digit numbers can be formed using the digits $0,1,2,3,4,5,6,7,8,$ and 9 if the first digit cannot be $0 ?$ Repeated digits are allowed.

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Problem 26

How many five-digit numbers can be formed using the digits $0,1,2,3,4,5,6,7,8,$ and 9 if the first digit cannot be 0 or 17 Repeated digits are allowed.

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Problem 27

In a consumer survey of 500 people, 200 indicated that they would be buying a major appliance within the next month, 150 indicated that they would buy a car, and 25 said that they would purchase both a major appliance and a car. How many will purchase neither? How many will purchase only a car?

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Problem 28

In a student survey, 200 indicated that they would attend Summer Session I and 150 indicated Summer Session II. If 75 students plan to attend both summer sessions and 275 indicated that they would attend neither session, how many students participated in the survey?

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Problem 29

In a survey of 100 investors in the stock market,
50 owned shares in IBM
40 owned shares in AT\&T
45 owned shares in GE
20 owned shares in both IBM and GE
15 owned shares in both AT\&T and GE
20 owned shares in both IBM and AT \& T
5 owned shares in all three
(a) How many of the investors surveyed did not have shares in any of the three companies?
(b) How many owned just IBM shares?
(c) How many owned just GE shares?
(d) How many owned neither IBM nor GE?
(e) How many owned cither IBM or AT\&T but no GE?

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Problem 30

Human blood is classified as either $\mathrm{Rh}+$ or $\mathrm{Rh}-.$ Blood is also classified by type: $\mathrm{A},$ if it contains an A antigen but not a $B$ antigen; $B$, if it contains a $B$ antigen but not an A antigen; AB, if it contains both A and B antigens; and $\mathrm{O}$, if it contains neither antigen. Draw a Venn diagram illustrating the various blood types. Based on this classification, how many different kinds of blood are there?

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Problem 31

The following data represent the marital status of males 18 years old and older in 2007 .
(a) Determine the number of males 18 years old and older who are widowed or divorced.
(b) Determine the number of males 18 years old and older who are married, widowed, or divorced.
(FIGURE CANNOT COPY)

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Problem 32

Demographics The following data represent the marital status of females 18 years old and older in 2007 .
(a) Determine the number of females 18 years old and older who are widowed or divorced.
(b) Determine the number of females 18 years old and older who are married, widowed, or divorced.
(FIGURE CANNOT COPY)

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Problem 33

As a financial planner, you are asked to select one stock each from the following groups: 8 DOW stocks, 15 NASDAQ stocks, and 4 global stocks. How many different portfolios are possible?

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Problem 34

Make up a problem different from any found in the text that requires the addition principle of counting to solve. Give it friend to solve and critique,

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Problem 35

Investigate the notion of counting as it relates to infinite sets. Write an essay on your findings.

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