 2.1P: A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an e...
 2.1STE: A cafeteria offers a threecourse meal consisting of an entree, a s...
 2.1TE: Prove the following relation
 2.2P: In an experiment, die is rolled continually until a 6 appears, at w...
 2.2STE: A customer visiting the suit department of a certain store will pur...
 2.2TE: Prove the following relationIf , then
 2.3P: Two dice are thrown. Let E be the event that the sum of the dice is...
 2.3STE: A deck of cards is dealt out. What is the probability that the 14th...
 2.3TE: Prove the following relation and
 2.4P: A, B, and C take turns flipping a coin. The first one to get a head...
 2.4STE: Let A denote the event that the midtown temperature in Los Angeles ...
 2.4TE: Prove the following relation and
 2.5P: A system is composed of 5 components, each of which is either worki...
 2.5STE: An ordinary deck of 52 cards is shuffled. What is the probability t...
 2.5TE: For any sequence of events E1, E2,..., define a new sequence F1,F2,...
 2.6P: A hospital administrator codes incoming patients suffering gunshot ...
 2.6STE: Urn A contains 3 red and 3 black balls, whereas urn B contains 4 re...
 2.6TE: Let E, F, and G be three events. Find expressions for the events so...
 2.7P: Consider an experiment that consists of determining the type of job...
 2.7STE: In a state lottery, a player must choose 8 of the numbers from 1 to...
 2.7TE: Use Venn diagrams(a) to simplify the expressions (E F)(E Fc);(b) to...
 2.8P: Suppose that A and B are mutually exclusive events for which P(A) =...
 2.8STE: From a group of 3 firstyear students, 4 sophomores, 4 juniors, and...
 2.8TE: Let S be a given set. If, for some k > 0, S1, S2,......Sk are mutua...
 2.9P: A retail establishment accepts either the American Express or the V...
 2.9STE: For a finite set A, let N(A) denote the number of elements in A.(a)...
 2.9TE: Suppose that an experiment is performed n times. For any event E of...
 2.10P: Sixty percent of the students at a certain school wear neither a ri...
 2.10STE: Consider an experiment that consists of 6 horses, numbered 1 throug...
 2.10TE: Prove that P(E F G)= P(E) + P(F) + P(G) P(ECFG) ? P(EFCG)? P(EFGC)...
 2.11P: A total of 28 percent of American males smoke cigarettes, 7 percent...
 2.11STE: A 5card hand is dealt from a wellshuffled deck of 52 playing card...
 2.11TE: If P(E)= .9 and P(F) = .8, show that P(EF) ? .7. In general, prove ...
 2.12P: An elementary school is offering 3 language classes: one in Spanish...
 2.12STE: A basketball team consists of 6 frontcourt and 4 backcourt players...
 2.12TE: Show that the probability that exactly one of the events E or F occ...
 2.13P: A certain town with a population of 100,000 has 3 newspapers: I, II...
 2.13STE: Suppose that a person chooses a letter at random from RESERVE and t...
 2.13TE: Prove that P(EFC) = P(E)? P(EF).
 2.14P: The following data were given in a study of a group of 1000 subscri...
 2.14STE: Prove Boole’s inequality.
 2.14TE: Prove Proposition 4.4 by mathematical induction.
 2.15P: If it is assumed that all poker hands are equally likely, what is t...
 2.15STE: Show that if
 2.15TE: An urn contains M white and N black balls. If a random sample of si...
 2.16P: Poker dice is played by simultaneously rolling 5 dice. Show that(a)...
 2.16STE: Let Tk(n) denote the number of partitions of the set {1,... ,n} int...
 2.16TE: Use induction to generalize Bonferroni’s inequality to n events. Th...
 2.17P: If 8 rooks (castles) are randomly placed on a chessboard, compute t...
 2.17STE: Five balls are randomly chosen, without replacement, from an urn th...
 2.17TE: Consider the matching problem, Example 5m, and define An to be the ...
 2.18P: Two cards are randomly selected from an ordinary playing deck. What...
 2.18STE: Four red, 8 blue, and 5 green balls are randomly arranged in a line...
 2.18TE: Let fn denote the number of ways of tossing a coin n times such tha...
 2.19P: Two symmetric dice have had two of their sides painted red, two pai...
 2.19STE: Ten cards are randomly chosen from a deck of 52 cards that consists...
 2.19TE: An urn contains n red and m blue balls. They are withdrawn one at a...
 2.20P: Suppose that you are playing blackjack against a dealer. In a fresh...
 2.20STE: Balls are randomly removed from an urn initially containing 20 red ...
 2.20TE: Consider an experiment whose sample space consists of a countably i...
 2.21P: A small community organization consists of 20 families, of which 4 ...
 2.21TE: Consider Example 5o, which is concerned with the number of runs of ...
 2.22P: Consider the following technique for shuffling a deck of n cards: F...
 2.23P: A pair of fair dice is rolled. What is the probability that the sec...
 2.24P: If two dice are rolled, what is the probability that the sum of the...
 2.25P: A pair of dice is rolled until a sum of either 5 or 7 appears. Find...
 2.26P: The game of craps is played as follows: A player rolls two dice. If...
 2.27P: An urn contains 3 red and 7 black balls. Players A and B withdraw b...
 2.28P: An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 bal...
 2.29P: An urn contains n white and m black balls, where n and m are positi...
 2.30P: The chess clubs of two schools consist of, respectively, 8 and 9 pl...
 2.31P: A 3person basketball team consists of a guard, a forward, and a ce...
 2.32P: A group of individuals containing b boys and g girls is lined up in...
 2.33P: A forest contains 20 elk, of which 5 are captured, tagged, and then...
 2.34P: The second Earl of Yarborough is reported to have bet at odds of 10...
 2.35P: Seven balls are randomly withdrawn from an urn that contains 12 red...
 2.36P: Two cards are chosen at random from a deck of 52 playing cards. Wha...
 2.37P: An instructor gives her class a set of 10 problems with the informa...
 2.38P: There are n socks, 3 of which are red, in a drawer. What is the val...
 2.39P: There are 5 hotels in a certain town. If 3 people check into hotels...
 2.40P: A town contains 4 people who repair televisions. If 4 sets break do...
 2.41P: If a die is rolled 4 limes, what is the probability that 6 comes up...
 2.42P: Two dice are thrown n times in succession. Compute the probability ...
 2.43P: (a) If N people, including A and B, are randomly arranged in a line...
 2.44P: Five people, designated as A, B, C, D, E, are arranged in linear or...
 2.45P: A woman has n keys, of which one will open her door.(a) If she trie...
 2.46P: How many people have to be in a room in order that the probability ...
 2.47P: If there are 12 strangers in a room, what is the probability that n...
 2.48P: Given 20 people, what is the probability that among the 12 months i...
 2.49P: A group of 6 men and 6 women is randomly divided into 2 groups of s...
 2.50P: In a hand of bridge, find the probability that you have 5 spades an...
 2.51P: Suppose that n balls are randomly distributed into N compartments. ...
 2.52P: A closet contains 10 pairs of shoes. If 8 shoes are randomly select...
 2.53P: If 4 married couples are arranged in a row, find the probability th...
 2.54P: Compute the probability that a bridge hand is void in at least one ...
 2.55P: Compute the probability that a hand of 13 cards contains(a) the ace...
 2.56P: Two players play the following game: Player A chooses one of the th...
Solutions for Chapter 2: A First Course in Probability 9th Edition
Full solutions for A First Course in Probability  9th Edition
ISBN: 9780321794772
Solutions for Chapter 2
Get Full SolutionsChapter 2 includes 97 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 97 problems in chapter 2 have been answered, more than 62036 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

`error (or `risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

Attribute
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

Backward elimination
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

Bimodal distribution.
A distribution with two modes

Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Central composite design (CCD)
A secondorder response surface design in k variables consisting of a twolevel factorial, 2k axial runs, and one or more center points. The twolevel factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a secondorder model.

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Conidence coeficient
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

Consistent estimator
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

Continuity correction.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Error of estimation
The difference between an estimated value and the true value.

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

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

Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

Harmonic mean
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .