A First Course in Probability9th EditionSheldon Ross Publisher: PEARSONISBN: 9780321794772
A First Course in Probability
Solutions for A First Course in Probability
Problem 1.1P:
a. How many different 7-place license plates are possible if the first 2 places are for letters and...Problem 1.2P:
How many outcome sequences are possible ten a die is rolled four times, where we say, for instance,...Problem 1.3P:
Twenty workers are to be assigned to 20 different jobs, one to each job. How many different...Problem 1.4P:
John, Jim, Jay, and Jack have formed a band consisting of 4 instruments if each of the boys can play...Problem 1.5P:
For years, telephone area codes in the United States and Canada consisted of a sequence of three...Problem 1.6P:
A well-known nursery rhyme starts as follows: As I was going to St. Ives I met a man with 7 wives....Problem 1.7P:
a. In how many ways can 3 boys and 3 girls sit in a row? b. In how many ways can 3 boys and 3 girls...Problem 1.8P:
When all letters are used, how many different letter arrangements can be made from the letters a....Problem 1.9P:
A child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. If the child puts...Problem 1.10P:
In how many ways can 8 people be seated in a row if a. there are no restrictions on the seating...Problem 1.11P:
In how many ways can 3 novels. 2 mathematics books, and 1 chemistry book be arranged on a bookshelf...Problem 1.12P:
Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to...Problem 1.13P:
Consider a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take...Problem 1.14P:
How many 5-card poker hands are there?Problem 1.15P:
A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women...Problem 1.16P:
A student has to sell 2 books from a collection of 6 math, 7 science, and 4 economics books. How...Problem 1.17P:
Seven different gifts are to be distributed among 10 children. How many distinct results are...Problem 1.18P:
A committee of 7, consisting of 2 Republicans, 2 Democrats, and 3 Independents, is to be chosen from...Problem 1.19P:
From a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. How...Problem 1.20P:
A person has 8 friends, of whom S will be invited to a party. a. How many choices are there if 2 of...Problem 1.21P:
Consider the grid of points shown at the top of the next column. Suppose that, starting at the point...Problem 1.22P:
In Problem 23, how many different paths are there from A to B that go through the point circled in...Problem 1.23P:
A psychology laboratory conducting dream research contains 3 rooms, with 2 beds in each room. If 3...Problem 1.24P:
Expand (3x2+y)5.Problem 1.25P:
The game of bridge is played by 4 players, each of w1om is dealt 13 cards. How many bridge deals are...Problem 1.26P:
Expand (x1+2x2+3x3)4.Problem 1.27P:
If 12 people are to be divided into 3 committees of respective sizes 3, 4, and 5, how many divisions...Problem 1.28P:
If 8 new teachers are to be divided among 4 schools, how many divisions are possible? What if each...Problem 1.29P:
Ten weight lifters are competing in a team weight-lifting contest. Of the lifters, 3 are from the...Problem 1.30P:
Delegates from 10 countries, including Russia, France, England, and the United States, are to be...Problem 1.31P:
If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? How...Problem 1.32P:
An elevator starts at the basement with 8 people (not including the elevator operator) and...Problem 1.33P:
We have 520.000 that must be invested among 4 possible opportunities. Each investment must be...Problem 1.34P:
Suppose that 10 fish are caught at a lake that contains 5 distinct types of fish. a. How many...Problem 1.2TE:
Two experiments are to be performed. The first can result in any one of m possible outcomes. If the...Problem 1.3TE:
In how many ways can r objects be selected from a set of n objects if the order of selection is...Problem 1.4TE:
There are (nr) different linear arrangements of n balls of which r are black and nr are white. Give...Problem 1.5TE:
Determine the number of vectors (x1,...,xn), such that each x1 is either 0 or 1 andi=1nxiKProblem 1.6TE:
How many vectors x1,...,xk are there for which each xi is a positive integer such that1xin and...Problem 1.7TE:
Give an analytic proof of Equation (4.1).Problem 1.8TE:
Prove that (n+mr)=(n0)(mr)+(n1)(mr1)+...+(nr)(m0) Hint: Consider a group of n men and m women. How...Problem 1.9TE:
Use Theoretical Exercise 8 I to prove that (2nn)=k=0n(nk)2Problem 1.10TE:
From a group of n people, suppose that we want to choose a committee of k,kn, one of whom is to be...Problem 1.11TE:
The following identity is known as Fermats combinatorial identity:(nk)=i=kn(i1k1)nk Give a...Problem 1.12TE:
Consider the following combinatorial identity: k=0nk(nk)=n2n1 a. Present a combinatorial argument...Problem 1.14TE:
From a set of n people, a committee of size j is to be chosen, and from this committee, a...Problem 1.15TE:
Let Hn(n) be the number of vectors x1,...,xk for which each xi is a positive integer satisfying 1xin...Problem 1.16TE:
Consider a tournament of n contestants in which the outcome is an ordering of these contestants,...Problem 1.17TE:
Present a combinatorial explanation of why (nr)=(nr,nr)Problem 1.18TE:
Argue that(nn1,n2,...,nr)=(n1n11,n2,...,nr)+(nn1,n21,...,nr)+...+(nn1,n2,...,nr1) Hint: Use an...Problem 1.19TE:
Prove the multinomial theorem.Problem 1.20TE:
In how many ways can n identical balls be distributed into r urns so that the ith urn contains at...Problem 1.21TE:
Argue that there are exactly (rk)(n1nr+k) solutions of x1+x2+...+xr=n for which exactly k of the xi...Problem 1.23TE:
Determine the number of vectors (xi,...,xn) such that each xi, is a nonnegative integer and i=1nxik.Problem 1.1STPE:
How many different linear arrangements are there of the letters A, B, C, D, E, F for which a. A and...Problem 1.2STPE:
If 4 Americans, 3 French people, and 3 British people are to be seated in a row, how many seating...Problem 1.3STPE:
A president. treasurer, and secretary. all different, are to be chosen from a club onsisting of 10...Problem 1.4STPE:
A student is to answer 7 out of 10 questions in an examination. How many choices has she? How many...Problem 1.5STPE:
In how many ways can a man divide 7 gifts among his 3 children if the eldest is to receive 3 gifts...Problem 1.6STPE:
How many different 7-place license plates are possible mien 3 of the entries are letters and 4 are...Problem 1.7STPE:
Give a combinatorial explanation of the identity(nr)=(nnr)Problem 1.8STPE:
Consider n-digit numbers where each digit is one of the 10 integers 0,1, ... ,9. How many such...Problem 1.9STPE:
Consider three classes, each consisting of n students. From this group of 3n students, a group of 3...Problem 1.10STPE:
How many 5-digit numbers can be formed from the integers 1,2,... ,9 if no digit can appear more than...Problem 1.11STPE:
From 10 married couples, we want to select a group of 6 people that is not allowed to contain a...Problem 1.12STPE:
A committee of 6 people is to be chosen from a group consisting of 7 men and 8 women. If the...Problem 1.13STPE:
An art collection on auction consisted of 4 Dalis, 5 van Goghs. and 6 Picassos, At the auction were...Problem 1.15STPE:
A total of n students are enrolled in a review course for the actuarial examination in probability....Problem 1.17STPE:
Give an analytic verification of (n2)=(k2)+k(nk)+(n+k2),1kn. Now, give a combinatorial argument for...Problem 1.18STPE:
In a certain community, there are 3 families consisting of a single parent and 1 child, 3 families...Browse All Chapters of This Textbook
Chapter 1 - Combinatorial AnalysisChapter 2 - Axioms Of ProbabilityChapter 3 - Conditional Probability And IndependenceChapter 4 - Random VariablesChapter 5 - Continuous Random VariablesChapter 6 - Jointly Distributed Random VariablesChapter 7 - Properties Of ExpectationChapter 8 - Limit TheoremsChapter 9 - Additional Topics In ProbabilityChapter 10 - Simulation
Book Details
Sheldon M. Ross is a professor in the Department of Industrial Engineering and Operations Research at the University of Southern California. He received his Ph.D. in statistics at Stanford University in 1968. He has published many technical articles and textbooks in the areas of statistics and applied probability. Among his texts are A First Course in Probability, Introduction to Probability Models, Stochastic Processes, and Introductory Statistics. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences , the Advisory Editor for International Journal of Quality Technology and Quantitative Management, and an Editorial Board Member of the Journal of Bond Trading and Management. He is a Fellow of the Institute of Mathematical Statistics and a recipient of the Humboldt US Senior Scientist Award.
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More Editions of This Book
Corresponding editions of this textbook are also available below:
EBK A FIRST COURSE IN PROBABILITY
9th Edition
ISBN: 9780321926678
A First Course In Probability
9th Edition
ISBN: 9789332519077
EBK A FIRST COURSE IN PROBABILITY
9th Edition
ISBN: 8220101467447
A First Course In Probability
5th Edition
ISBN: 9780137463145
A First Course in Probability
8th Edition
ISBN: 9780136033134
A First Course In Probability, Global Edition
10th Edition
ISBN: 9781292269207
FIRST COURSE IN PROBABILITY (LOOSELEAF)
10th Edition
ISBN: 9780134753751
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753683
A Second Course in Probability
7th Edition
ISBN: 9780979570407
First Course In Probability, A (7th Edition)
7th Edition
ISBN: 9780131856622
A First Course In Probability (6th Edition)
6th Edition
ISBN: 9780130338518
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