Applied Mathematics: For the Managerial, Life, and Social Sciences

Soo T. Tan

Chapter 8

Additional Topics in Probability - all with Video Answers

Educators

Section 1

Use of Counting Techniques in Probability

Problem 1

Find the probability of the given event.
The coin lands heads all five times.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 2

Find the probability of the given event.
The coin lands heads exactly once.

Harsh Gadhiya

Numerade Educator

Problem 3

Find the probability of the given event.
The coin lands heads at least once.

Harsh Gadhiya

Numerade Educator

Problem 4

Find the probability of the given event.
The coin lands heads more than once.

Harsh Gadhiya

Numerade Educator

Problem 5

Find the probability of the given event.
A pair is drawn.

Lucas Finney

Numerade Educator

Problem 6

Find the probability of the given event.
A pair is not drawn.

Lucas Finney

Numerade Educator

Problem 7

Find the probability of the given event.
Two black cards are drawn.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 8

Find the probability of the given event.
Two cards of the same suit are drawn.

Lourence Gonhovi

Lourence Gonhovi

Numerade Educator

Problem 9

Find the probability of the given event.
Two of the balls are white and two are blue.

James Macpherson

James Macpherson

Numerade Educator

Problem 10

Find the probability of the given event.
All of the balls are blue.

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 11

Find the probability of the given event.
Exactly three of the balls are blue.

Goutam Chand

Numerade Educator

Problem 12

Find the probability of the given event.
Two or three of the balls are white.

Goutam Chand

Numerade Educator

Problem 13

Find the probability that a family with three children will have the given composition.
Two boys and one girl

Jeff Vermeire

Numerade Educator

Problem 14

Find the probability that a family with three children will have the given composition.
At least one girl

Jeff Vermeire

Numerade Educator

Problem 15

Find the probability that a family with three children will have the given composition.
No girls

Jeff Vermeire

Numerade Educator

Problem 16

Find the probability that a family with three children will have the given composition.
The two oldest children are girls.

Jeff Vermeire

Numerade Educator

Problem 17

An exam consists of ten true-or-false questions. If a student guesses at every answer, what is the probability that he or she will answer exactly six questions correctly?

AG

Ankit Gupta

Numerade Educator

Problem 18

Jacobs \& Johnson, an accounting firm, employs 14 accountants, of whom 8 are CPAs. If a delegation of 3 accountants is randomly selected from the firm to attend a conference, what is the probability that 3 CPAs will be selected?

Hossam Mohamed

Numerade Educator

Problem 19

Two light bulbs are selected at random from a lot of 24 , of which 4 are defective. What is the probability that
a. Both of the light bulbs are defective?
b. At least 1 of the light bulbs is defective?

Mir Afzal

Numerade Educator

Problem 20

A customer at Cavallaro's Fruit Stand picks a sample of 3 oranges at random from a crate containing 60 oranges, of which 4 are rotten. What is the probability that the sample contains 1 or more rotten oranges?

Carson Merrill

Numerade Educator

Problem 21

A shelf in the Metro Department Store contains 80 colored ink cartridges for a popular ink-jet printer. Six of the cartridges are defective. If a customer selects 2 cartridges at random from the shelf, what is the probability that
a. Both are defective?
b. At least 1 is defective?

Rashmi Sinha

Numerade Educator

Problem 22

Electronic baseball games manufactured by Tempco Electronics are shipped in lots of 24 . Before shipping, a quality-control inspector randomly selects a sample of 8 from each lot for testing. If the sample contains any defective games, the entire lot is rejected. What is the probability that a lot containing exactly 2 defective games will still be shipped?

Nick Johnson

Numerade Educator

Problem 23

The City Transit Authority plans to hire 12 new bus drivers. From a group of 100 qualified applicants, of whom 60 are men and 40 are women, 12 names are to be selected by lot. Suppose that Mary and John Lewis are among the 100 qualified applicants.
a. What is the probability that Mary's name will be selected? That both Mary's and John's names will be selected?
b. If it is stipulated that an equal number of men and women are to be selected $(6$ men from the group of 60 men and 6 women from the group of 40 women), what is the probability that Mary's name will be selected? That Mary's and John's names will be selected?

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 24

The City Housing Authority has received 50 applications from qualified applicants for eight lowincome apartments. Three of the apartments are on the north side of town, and five are on the south side. If the apartments are to be assigned by means of a lottery, what is the probability that a. A specific qualified applicant will be selected for one of these apartments?
b. Two specific qualified applicants will be selected for apartments on the same side of town?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 25

A student studying for a vocabulary test knows the meanings of 12 words from a list of 20 words. If the test contains 10 words from the study list, what is the probability that at least 8 of the words on the test are words that the student knows?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 26

Four different written driving tests are administered by the Motor Vehicle Department. One of these four tests is selected at random for each applicant for a driver's license. If a group consisting of two women and three men apply for a license, what is the probability that
a. Exactly two of the five will take the same test?
b. The two women will take the same test?

Nick Johnson

Numerade Educator

Problem 27

A druggist wishes to select three brands of aspirin to sell in his store. He has five major brands to choose from: A, B, C, D, and E. If he selects the three brands at random, what is the probability that he will select
a. Brand $\mathrm{B}$ ?
b. Brands $\mathrm{B}$ and $\mathrm{C}$ ?
c. At least one of the two brands $\mathrm{B}$ and $\mathrm{C}$ ?

Jennifer Stoner

Jennifer Stoner

Numerade Educator

Problem 28

In the game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack.
a. If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?
b. If a player is dealt 2 cards from 2 well-shuffled standard decks, what is the probability that the player will receive a blackiack?

Steven Clarke

Numerade Educator

Problem 29

Refer to Exercise 25, Section $7.3$, where the "lucky dollar" slot machine was described. What is the probability that the three "lucky dollar" symbols will appear in the window of the slot machine?

Charles Carter

Numerade Educator

Problem 30

In 1959 a world record was set for the longest run on an ungaffed (fair) roulette wheel at the El San Juan Hotel in Puerto Rico. The number 10 appeared six times in a row. What is the probability of the occurrence of this event? (Assume that there are 38 equally likely outcomes consisting of the numbers $1-36,0$, and 00 .)

AG

Ankit Gupta

Numerade Educator

Problem 31

Find the probability that a ticket holder has the indicated winning ticket.
All four digits in exact order (the grand prize)

Sarah Wharton

Numerade Educator

Problem 32

Find the probability that a ticket holder has the indicated winning ticket.
Two specified, consecutive digits in exact order (the first two digits, the middle two digits, or the last two digits)

Sarah Wharton

Numerade Educator

Problem 33

Find the probability that a ticket holder has the indicated winning ticket.
One digit (the first, second, third, or fourth digit)

Sarah Wharton

Numerade Educator

Problem 34

Find the probability that a ticket holder has the indicated winning ticket.
Three digits in exact order

Sarah Wharton

Numerade Educator

Problem 35

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand?
A straight flush (Note that an ace may be played as either a high or low card in a straight sequence-that is, $\mathrm{A}, 2,3$,
4, 5 or $10, \mathrm{~J}, \mathrm{Q}, \mathrm{K}, \mathrm{A}$. Hence, there are ten possible sequences for a straight in one suit.)

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 36

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand?
A straight (but not a straight flush)

Dalia Rodriguez

Dalia Rodriguez

Numerade Educator

Problem 37

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand?
A flush (but not a straight flush)

James Chok

Numerade Educator

Problem 38

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand?
Four of a kind

Hossam Mohamed

Numerade Educator

Problem 39

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand?
A full house

Lourence Gonhovi

Lourence Gonhovi

Numerade Educator

Problem 40

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand?
Two pairs

Lourence Gonhovi

Lourence Gonhovi

Numerade Educator

Problem 41

There are 12 signs of the Zodiac: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. Each sign corresponds to a different calendar period of approximately 1 month. Assuming that a person is just as likely to be born under one sign as another, what is the probability that in a group of five people at least two of them
a. Have the same sign?
b. Were born under the sign of Aries?

Nick Johnson

Numerade Educator

Problem 42

What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday?

Sanchit Jain

Numerade Educator

Problem 43

Fifty people are selected at random. What is the probability that none of the people in this group have the same birthday?

Muhammad Nawaz

Numerade Educator

Problem 44

There were 42 different presidents of the United States from 1789 through 2000 . What is the probability that at least two of them had the same birthday? Compare your calculation with the facts by checking an almanac or some other source.

Sanchit Jain

Numerade Educator