 1.1P: (a) How many different 7place license plates are possible if the f...
 1.1STE: How many different linear arrangements are there of the letters A, ...
 1.1TE: Prove the generalized version of the basic counting principle.
 1.2P: How many outcome sequences are possible when a die is rolled four t...
 1.2STE: If 4 Americans, 3 French people, and 3 British people are to be sea...
 1.2TE: Two experiments are to be performed. The first can result in any on...
 1.3P: Twenty workers are to be assigned to 20 different jobs, one to each...
 1.3STE: A president, treasurer, and secretary, all different, are to be cho...
 1.3TE: In how many ways can r objects be selected from a set of n objects ...
 1.4P: John, Jim, Jay, and Jack have formed a band consisting of 4 instrum...
 1.4STE: A student is to answer 7 out of 10 questions in an examination. How...
 1.4TE: There are different linear arrangements of n balls of which r are b...
 1.5P: For years, telephone area codes in the United States and Canada con...
 1.5STE: In how many ways can a man divide 7 gifts among his 3 children if t...
 1.5TE: Determine the number of vectors (x1,... ,xn), such that each xi is ...
 1.6P: A wellknown nursery rhyme starts as follows:“As I was going to St....
 1.6STE: How many different 7place license plates are possible when 3 of th...
 1.6TE: How many vectors x1,...,xk are there for which each xi, is a positi...
 1.7P: (a) In how many ways can 3 boys and 3 girls sit in a row?(b) In how...
 1.7STE: Give a combinatorial explanation of the identity
 1.7TE: Give an analytic proof of Equation (4.1).
 1.8P: How many different letter arrangements can be made from the letters...
 1.8STE: Consider ndigit numbers where each digit is one of the 10 integers...
 1.8TE: Prove that
 1.9P: A child has 12 blocks, of which 6 are black, 4 are red, 1 is white,...
 1.9STE: Consider three classes, each consisting of n students. From this gr...
 1.9TE: Use Theoretical Exercise 1 to prove that Exercise 1Prove that
 1.10P: In how many ways can 8 people be seated in a row if(a) there are no...
 1.10STE: How many 5digit numbers can be formed from the integers 1,2,... ,9...
 1.10TE: From a group of n people, suppose that we want to choose a committe...
 1.11P: In how many ways can 3 novels, 2 mathematics books, and 1 chemistry...
 1.11STE: From 10 married couples, we want to select a group of 6 people that...
 1.11TE: The following identity is known as Fermat’s combinatorial identity:...
 1.12P: Five separate awards (best scholarship, best leadership qualities, ...
 1.12STE: A committee of 6 people is to be chosen from a group consisting of ...
 1.12TE: Consider the following combinatorial identity: (a) Present a combin...
 1.13P: Consider a group of 20 people. If everyone shakes hands with everyo...
 1.13STE: An art collection on auction consisted of 4 Dalis, 5 van Goghs, and...
 1.13TE: Show that, for n > 0,
 1.14P: How many 5card poker hands are there?
 1.14STE: Determine the number of vectors (x1,... ,xn) such that each xi is a...
 1.14TE: From a set of n people, a committee of size j is to be chosen, and ...
 1.15P: A dance class consists of 22 students, of which 10 are women and 12...
 1.15STE: A total of n students are enrolled in a review course for the actua...
 1.15TE: Let Hk(n) be the number of vectors x1,...,xk for which each xi is a...
 1.16P: A student has to sell 2 books from a collection of 6 math, 7 scienc...
 1.16STE: How many subsets of size 4 of the set S = {1,2,..., 20} contain at ...
 1.16TE: Consider a tournament of n contestants in which the outcome is an o...
 1.17P: Seven different gifts are to be distributed among 10 children. How ...
 1.17STE: Give an analytic verification of Now, give a combinatorial argument...
 1.17TE: Present a combinatorial explanation of why solution of .
 1.18P: A committee of 7, consisting of 2 Republicans, 2 Democrats, and 3 I...
 1.18STE: In a certain community, there are 3 families consisting of a single...
 1.18TE: Argue that
 1.19P: From a group of 8 women and 6 men, a committee consisting of 3 men ...
 1.19STE: If there are no restrictions on where the digits and letters are pl...
 1.19TE: Prove the multinomial theorem.
 1.20P: A person has 8 friends, of whom 5 will be invited to a party.(a) Ho...
 1.20STE: Verify that the equality when n = 3, r = 2, and then show that it a...
 1.20TE: In how many ways can n identical balls be distributed into r urns s...
 1.21P: Consider the grid of points shown at the top of the next column. Su...
 1.21TE: Argue that there are exactly solutions of for which exactly k of th...
 1.22P: In 1, how many different paths are there from A to B that go throug...
 1.22TE: Consider a function f(x1,...,xn) of n variables. How many different...
 1.23P: A psychology laboratory conducting dream research contains 3 rooms,...
 1.23TE: Determine the number of vectors (x1,... ,xn) such that each xi is a...
 1.24P: Expand (3x2 + y)5.
 1.25P: The game of bridge is played by 4 players, each of whom is dealt 13...
 1.26P: Expand (x1 + 2x2 + 3x3)4.
 1.27P: If 12 people are to be divided into 3 committees of respective size...
 1.28P: If 8 new teachers are to be divided among 4 schools, how many divis...
 1.29P: Ten weight lifters are competing in a team weightlifting contest. O...
 1.30P: Delegates from 10 countries, including Russia, France, England, and...
 1.31P: If 8 identical blackboards are to be divided among 4 schools, how m...
 1.32P: An elevator starts at the basement with 8 people (not including the...
 1.33P: We have $20,000 that must be invested among 4 possible opportunitie...
 1.34P: Suppose that 10 fish are caught at a lake that contains 5 distinct ...
Solutions for Chapter 1: A First Course in Probability 9th Edition
Full solutions for A First Course in Probability  9th Edition
ISBN: 9780321794772
Solutions for Chapter 1
Get Full SolutionsChapter 1 includes 77 full stepbystep solutions. This textbook survival guide was created for the textbook: A First Course in Probability , edition: 9. A First Course in Probability was written by and is associated to the ISBN: 9780321794772. Since 77 problems in chapter 1 have been answered, more than 63056 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

Bernoulli trials
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

Chisquare test
Any test of signiicance based on the chisquare distribution. The most common chisquare tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

Coeficient of determination
See R 2 .

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Defectsperunit control chart
See U chart

Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

Empirical model
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

Factorial experiment
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

False alarm
A signal from a control chart when no assignable causes are present

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

Generating function
A function that is used to determine properties of the probability distribution of a random variable. See Momentgenerating function

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .