A First Course in Probability9th EditionSheldon Ross Publisher: PEARSONISBN: 9780321794772
A First Course in Probability
Solutions for A First Course in Probability
Problem 2.1P:
A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking...Problem 2.2P:
In an experiment, die is rolled continually until a 6 appears, at which point the experiment stops....Problem 2.3P:
Two dice are thrown. Let E be the event that the sum of the dice is odd, let F be the event that at...Problem 2.4P:
A, B, and C take turns flipping a coin. The first one to get a head wins. The sample space of this...Problem 2.5P:
A system is composed of 5 components, each of which is either working or failed. Consider an...Problem 2.6P:
A hospital administrator codes incoming patients suffering gunshot wounds according to whether they...Problem 2.7P:
Consider an experiment that consists of determining the type of job-either blue collar or white...Problem 2.8P:
Suppose that A and B are mutually exclusive events for which P(A) = .3 and P(B) = .5. What is the...Problem 2.9P:
A retail establishment accepts either the American Express or the VISA credit card. A total of 24...Problem 2.10P:
Sixty percent of the students at a certain school wear neither a ring nor a necklace. Twenty percent...Problem 2.11P:
A total of 28 percent of American males smoke cigarettes. 7 percent smoke cigars, and 5 percent...Problem 2.12P:
An elementary school is offering 3 language classes: one in Spanish. one In French. and one in...Problem 2.13P:
A certain town with a population of 100.000 has 3 newspapers: I, II, and Ill. The proportions of...Problem 2.14P:
The following data were given in a study of a group of 1000 subscribers to a certain magazine: In...Problem 2.15P:
If it is assumed that all (525) poker hands are equally likely, what is the probability of being...Problem 2.16P:
Poker dice is played by simultaneously rolling 5 dice. Show that a. P{no two alike} = .0926; b....Problem 2.17P:
Twenty five people, consisting of 15 women and 10 men are lined up in a random order. Find the...Problem 2.18P:
Two cards are randomly selected from an ordinary playing deck. What is the probability that they...Problem 2.19P:
Two symmetric dice have had two of their sides painted red, two painted black, one painted yellow,...Problem 2.20P:
Suppose that you are playing blackjack against a dealer. In a freshly shuffled deck, what is the...Problem 2.21P:
A small community organization consists of 20 families, of which 4 have one child. 8 have two...Problem 2.22P:
Consider the following technique for shuffling a deck of n cards: F of any initial ordering of the...Problem 2.23P:
A pair of fair dice is rolled. What is the probability that the second die lands on a higher value...Problem 2.24P:
It two dice are rolled, what is the probability that the sum of the upturned faces equals 1? Find it...Problem 2.25P:
A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs...Problem 2.26P:
The game of craps is played as follows: A player rolls two dice. If the sum of the dice is either a...Problem 2.27P:
An urn contains 3 red and 7 black balls. Players A and B withdraw balls from the urn consecutively...Problem 2.28P:
An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is...Problem 2.29P:
An urn contains n white and m black balls, where n and m are positive numbers. a. If two balls are...Problem 2.30P:
The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each...Problem 2.31P:
A 3-person basketball team consists of a guard, a forward, and a center. a. If a person is chosen at...Problem 2.32P:
A group of individuals containing b boys and g girls is lined up in random order: that is, each of...Problem 2.33P:
A forest contains 20 elk, of which 5 are captured, tagged, and then released. A certain time later,...Problem 2.34P:
The second Earl of Yarborough is reported to have bet at odds of 1000 to 1 that a bridge hand of 13...Problem 2.35P:
Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls....Problem 2.36P:
Two cards are chosen at random from a deck of 52 playing cards. What is the probability that they a....Problem 2.37P:
An instructor gives her class a set of 10 problems with the Information that the final exam will...Problem 2.38P:
There are n socks. 3 of which are red, in a drawer. What is the value of n if, when 2 of the socks...Problem 2.39P:
There are 5 hotels in a certain town. If 3 people check into hotels in a day, what is the...Problem 2.40P:
A town contains 4 people who repair televisions. If 4 sets break down, what is the probability that...Problem 2.42P:
Two dice are thrown n times in succession. Compute the probability that double 6 appears at least...Problem 2.43P:
a. If N people, including A and B, are randomly arranged in a line, what is the probability that A...Problem 2.44P:
Five people, designated as A, B, C, D, E, are arranged in linear order. Assuming that each possible...Problem 2.45P:
A woman has n keys, of which one will open her door. a. If she tries the keys at random, discarding...Problem 2.46P:
How many people have to be in a room in order that the probability that at least two of them...Problem 2.47P:
Suppose that 5 of the numbers 1, 2,..., 14 are chosen. Find the probability that 9 is the third...Problem 2.48P:
Given 20 people, what is the probability that among the 12 months in the year, there are 4 months...Problem 2.49P:
A group of 6 men and 6 women is randomly divided into 2 groups of size 6 each. What is the...Problem 2.50P:
In a hand of bridge, find the probability that you have 5 spades and your partner has the remaining...Problem 2.51P:
Suppose that n balls are randomly distributed into N compartments. Find the probability that m balls...Problem 2.52P:
A closet contains 10 pairs of shoes. If 8 shoes are randomly selected, what is the probability that...Problem 2.53P:
If 4 married couples are arranged in a row, find the probability that no husband sits next to his...Problem 2.54P:
Compute the probability that a bridge hand is void in at least one suit. Note that the answer is not...Problem 2.55P:
Compute the probability that a hand of 13 cards contains a. the ace and king of at least one suit:...Problem 2.56P:
Two players play the following game: Player A chooses one of the three spinners pictured in Figure...Problem 2.1TE:
Prove the following relations: EFEEFProblem 2.2TE:
Prove the following relations: If EF, then FCEC.Problem 2.3TE:
Prove the following relations: 3. F=FEFEC and EF=EECF ,Problem 2.5TE:
For any sequence of events E1,E2,..., define a new sequence F1,F2,... of disjoint events (that is....Problem 2.6TE:
Let E, F, and C be three events. Find expressions for the events so that. of E, F, and C, a. only E...Problem 2.7TE:
Use Venn diagrams a. to simplify the expression (EF)(EFC); b. to prove DeMorgans laws for events E...Problem 2.9TE:
Suppose that an experiment is performed n times For any event E of the sample space. let n(E) denote...Problem 2.11TE:
If P(E)=.9 and P(F)=.8, show that P(EF).7. In general, prove Bonferronis inequality,...Problem 2.12TE:
Show that the probability that exactly one of the events E or F occurs equalsP(E)+P(F)2P(EF).Problem 2.13TE:
Prove that P(EF)=P(E)P(EF).Problem 2.14TE:
Prove Proposition 4.4 by mathematical induction.Problem 2.15TE:
An urn contains M white and N black balls. If a random sample of size r is chosen, what is the...Problem 2.17TE:
Consider the matching problem. Example 5m, and define AN to be the number of ways in which the N men...Problem 2.18TE:
Let fn, denote the number of ways of tossing a coin n times such that successive heads never appear....Problem 2.19TE:
An urn contains n red and m blue balls. They are withdrawn one at a time until a total of r, rn red...Problem 2.20TE:
Consider an experiment whose sample space consists of a countably infinite number of points. Show...Problem 2.21TE:
Consider Example 50, which is concerned with the number of runs of wins obtained when n wins and m...Problem 2.1STPE:
A cafeteria offers a three-course meal consisting of an entree. a starch, and a dessert. The...Problem 2.2STPE:
A customer visiting the suit department of a certain store will purchase a suit with probability...Problem 2.3STPE:
A deck of cards is dealt out. What is the probability that the 14th card dealt is an ace? What is...Problem 2.4STPE:
Let A denote the event that the midtown temperature in Los Angeles is 70F, and let B denote the...Problem 2.5STPE:
An ordinary deck of 52 cards is shuffled. What is the probability that the top four cards have a....Problem 2.6STPE:
Urn A contains 3 red and 3 black balls, whereas urn B contains 4 red and 6 black balls. If a ball is...Problem 2.7STPE:
In a state lottery, a player must choose 8 of the numbers from 1 to 40. The lottery commission then...Problem 2.8STPE:
From a group of 3 first-year students, 4 sophomores, 4 juniors, and 3 seniors, a committee of size 4...Problem 2.9STPE:
For a finite set A, let N(A) denote the number of elements in A. a. Show that N(AB)=N(A)+N(B)N(AB)...Problem 2.10STPE:
Consider an experiment that consists of 6 horses, numbered 1 through 6, running a race, and suppose...Problem 2.11STPE:
A 5-card hand is dealt from a well-shuffled deck of 52 playing cards. What is the probability that...Problem 2.12STPE:
A basketball team consists of 6 frontcourt and 4 backcourt players. If players are divided into...Problem 2.13STPE:
Suppose that a person chooses a letter at random from R E S E R V E and then chooses one at random...Problem 2.14STPE:
Prove Booles inequality P(i=1Ai)i=1P(Ai)Problem 2.15STPE:
Show that if P(Ai)=1 for all i1, then P(i=1Ai)=1.Problem 2.16STPE:
Let Tk(n) denote the number of partitions of the set {1,...,n} into k nonempty subsets, where 1kn....Problem 2.17STPE:
Five balls are randomly chosen, without replacement, from an urn that contains 5 red, 6 white, and 7...Problem 2.18STPE:
Four red, 8 blue, and 5 green balls are randomly arranged in a line. a. What is the probability that...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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