Excursions in Modern Mathematics (9th Edition)
Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 16, Problem 1E

Using set notation, write out the sample space for each of the following random experiments.

a. A coin is tossed three times in a row. The observation is how the coin lands (H or T ) on each toss.

b. A basketball player shoots three consecutive free throws. The observation is the result of each free throw ( s for success, f for failure).

c. A coin is tossed three times in a row. The observation is the number of times the coin comes up tails.

d. A basketball player shoots three consecutive free throws. The observation is the number of successes.

Expert Solution
Check Mark
To determine

(a)

To calculate:

The Sample Space for a coin tossed three times.

Answer to Problem 1E

Solution:

The sample space is S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} for a coin tossed 3 times.

Explanation of Solution

Procedure used:

When a coin is tossed three times, the outcome in each toss is either head (H) or tail (T).

There is one way to get 3 heads: {HHH}

There are 3 ways to get 2 heads: {HHT,THH,HTH}

There is 1 way to get 3 tails: {TTT}

There are 3 ways to get 1 head:{HTT,THT,TTH}

The Sample Space of a sequence of three fair coin tosses is all 23 possible sequences of outcomes:

S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

So there are 8 events in the sample space. If the coin tossed is fair than each event is equally possible.

Given:

A coin is given for tossing.

Conclusion:

Thus, the sample space is S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} for a coin tossed 3 times.

Expert Solution
Check Mark
To determine

(b)

To calculate:

The Sample Space for three throws of basketball.

Answer to Problem 1E

Solution:

The Sample Space of a sequence of three consecutive free throws is S={sss,ssf,sfs,sff,fsf,fss,ffs,fff}.

Explanation of Solution

Given:

A basketball player shoots three consecutive free throws.

Calculation:

The outcome in each throw is either success (s) or failure (f).

There is one way to get 3 successes: {sss}

There are 3 ways to get 2 successes: {ssf,fss,sfs}

There is 1 way to get 3 failures: {fff}

There are 3 ways to get 1 success: {sff,fsf,ffs}

The Sample Space of a sequence of three consecutive free throws is all 23 possible sequences of outcomes:

S={sss,ssf,sfs,sff,fsf,fss,ffs,fff}

So there are 8 events in the sample space.

Conclusion:

Thus, the Sample Space of a sequence of three consecutive free throws is S={sss,ssf,sfs,sff,fsf,fss,ffs,fff}.

Expert Solution
Check Mark
To determine

(c)

To calculate:

The Sample Space for number of times the coin comes up a tail.

Answer to Problem 1E

Solution:

The Sample Space of the number of times the coin comes up tails is,

S={0,1,2,3}

Explanation of Solution

Given:

A coin is given for tossing.

Calculation:

When a coin is tossed three times, the outcome in each toss is either head (H) or tail (T).

Numbers of ways to get tail are:

No tail, one tail, two tails, and three tails in a sequence of three fair coin.

The Sample Space of the number of times the coin comes up tails is,

S={0,1,2,3}

Conclusion:

Thus, the Sample Space of the number of times the coin comes up tails is,

S={0,1,2,3}

Expert Solution
Check Mark
To determine

(d)

To calculate:

The Sample Space of the number of times the free throw results in success.

Answer to Problem 1E

Solution:

The Sample Space of the number of times the free throw results in success is,

S={0,1,2,3}

Explanation of Solution

Given:

A coin is given for tossing.

Calculation:

When a ball is thrown three times, the outcome in each throw is either success (s) or failure (f).

Numbers of ways to get success:

No free throw results in success, one success, two successes, and three successes in a sequence of three free throws.

The Sample Space of the number of times the free throw results in success is,

S={0,1,2,3}

Conclusion:

Thus, the Sample Space of the number of times the free throw results in success is,

S={0,1,2,3}

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Refer to page 311 for a sequence of functions defined on a given interval. Instructions: • Analyze whether the sequence converges pointwise and/or uniformly on the given interval. • Discuss the implications of uniform convergence for integration and differentiation of the sequence. • Provide counterexamples if any condition fails. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qo Hazb9tC440 AZF/view?usp=sharing]
Refer to page 310 for a matrix and its associated system of differential equations. Instructions: • Find the eigenvalues of the given matrix and classify the stability of the system (e.g., stable, • unstable, saddle point). Discuss the geometric interpretation of eigenvalues in the context of system behavior. • Provide conditions under which the system exhibits periodic solutions. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]
Refer to page 313 for a nonlinear differential equation and its linear approximation. Instructions: • Linearize the given nonlinear system around the equilibrium points. • Analyze the stability of each equilibrium using the Jacobian matrix and its eigenvalues. • Discuss the limitations of linearization for determining global behavior. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]

Chapter 16 Solutions

Excursions in Modern Mathematics (9th Edition)

Ch. 16 - A coin is tossed three times in a row The...Ch. 16 - A student randomly guesses the answers to a...Ch. 16 - A pair of dice is rolled. The observation is the...Ch. 16 - A card is drawn out of a standard deck of 52...Ch. 16 - A coin is tossed 10 times in a row. The...Ch. 16 - Five candidates (A,B,C,D,andE) have a chance to be...Ch. 16 - A California license plate starts with a digit...Ch. 16 - A computer password consists of four letters A...Ch. 16 - Jack packs two pairs of shoes, one pair of boots,...Ch. 16 - A French restaurant offers a menu consisting of...Ch. 16 - A set of reference books consists of eight volumes...Ch. 16 - Nine people four men and five women line up at a...Ch. 16 - 7. Nine people four men and five women line up at...Ch. 16 - Prob. 24ECh. 16 - Determine the number of outcomes N in each sample...Ch. 16 - Determine the number of outcomes N in each sample...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - A major league baseball team roster consists of 40...Ch. 16 - Bob has 20 different dress shirts in his wardrobe....Ch. 16 - Consider the sample space S={o1,o2,o3,o4,o5}....Ch. 16 - Consider the sample space S={o1,o2,o3,o4}. Suppose...Ch. 16 - Four candidates are running for mayor of...Ch. 16 - Seven horses A, B, C, D, E, F, and G are running...Ch. 16 - An honest coin is tossed three times in a row....Ch. 16 - A student randomly guesses the answers to a...Ch. 16 - A pair of honest dice is rolled. Find the...Ch. 16 - A card is drawn at random out of a well-shuffled...Ch. 16 - An honest coin is tossed 10 times in a row. Find...Ch. 16 - Five candidates A, B, C, D, and E have a chance to...Ch. 16 - A student takes a 10-question true-or-false quiz...Ch. 16 - Suppose that the probability of giving birth to a...Ch. 16 - The Tasmania State University glee club has 15...Ch. 16 - Ten professional basketball teams are...Ch. 16 - An honest coin is tossed 10 times in a row. The...Ch. 16 - Imagine a game in which you roll an honest die...Ch. 16 - Find the odds of each of the following events. a....Ch. 16 - Find the odds of each of the following events. a....Ch. 16 - In each case, find the probability of an event E...Ch. 16 - In each case, find the probability of an event E...Ch. 16 - Prob. 53ECh. 16 - Table 16-19 shows the aggregate scores of a golf...Ch. 16 - At Thomas Jefferson High School, the student body...Ch. 16 - In 2005 the Middletown Zoo averaged 4000 visitors...Ch. 16 - Prob. 57ECh. 16 - A basketball player shoots two consecutive free...Ch. 16 - Prob. 59ECh. 16 - A pair of honest dice is rolled once. Find the...Ch. 16 - Suppose that you roll a pair of honest dice. If...Ch. 16 - On an American roulette wheel, there are 18 red...Ch. 16 - On an American roulette wheel, there are 38...Ch. 16 - Suppose that you roll a single die. If an odd...Ch. 16 - Prob. 65ECh. 16 - Jackie is buying a new MP3 player from Better Buy....Ch. 16 - The service history of the Prego SUV is as...Ch. 16 - An insurance company plans to sell a 250,000...Ch. 16 - The ski club at Tasmania State University has 35...Ch. 16 - Prob. 70ECh. 16 - Prob. 71ECh. 16 - Two teams call them X and Y play against each...Ch. 16 - An urn contains seven red balls and three blue...Ch. 16 - Prob. 74ECh. 16 - Prob. 75ECh. 16 - A draw poker hand consists of 5 cards taken from a...Ch. 16 - Prob. 77ECh. 16 - Prob. 78ECh. 16 - Yahtzee. Yahtzee is a dice game in which five...Ch. 16 - In head-to-head, 7-card stud poker you make your...

Additional Math Textbook Solutions

Find more solutions based on key concepts
Find all solutions of each equation in the interval .

Precalculus: A Unit Circle Approach (3rd Edition)

For Problems 23-28, write in simpler form, as in Example 4. logbFG

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

1. How is a sample related to a population?

Elementary Statistics: Picturing the World (7th Edition)

Testing Hypotheses. In Exercises 13-24, assume that a simple random sample has been selected and test the given...

Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)

Knowledge Booster
Background pattern image
Math
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Text book image
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Probability & Statistics (28 of 62) Basic Definitions and Symbols Summarized; Author: Michel van Biezen;https://www.youtube.com/watch?v=21V9WBJLAL8;License: Standard YouTube License, CC-BY
Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=SkidyDQuupA;License: Standard YouTube License, CC-BY