 3.3.1: Two fair dice are rolled. What is the conditionalprobability that a...
 3.3.2: If two fair dice are rolled, what is the conditionalprobability tha...
 3.3.3: Use Equation (2.1) to compute, in a hand ofbridge, the conditional ...
 3.3.4: What is the probability that at least one of a pair offair dice lan...
 3.3.5: An urn contains 6 white and 9 black balls. If 4 ballsare to be rand...
 3.3.6: Consider an urn containing 12 balls, of which 8are white. A sample ...
 3.3.7: The king comes from a family of 2 children. Whatis the probability ...
 3.3.8: A couple has 2 children. What is the probabilitythat both are girls...
 3.3.9: Consider 3 urns. Urn A contains 2 white and 4 redballs, urn B conta...
 3.3.10: Three cards are randomly selected, withoutreplacement, from an ordi...
 3.3.11: Two cards are randomly chosen without replacementfrom an ordinary d...
 3.3.12: A recent college graduate is planning to take thefirst three actuar...
 3.3.13: Suppose that an ordinary deck of 52 cards (whichcontains 4 aces) is...
 3.3.14: An urn initially contains 5 white and 7 black balls.Each time a bal...
 3.3.15: An ectopic pregnancy is twice as likely to developwhen the pregnant...
 3.3.16: Ninetyeight percent of all babies survive delivery.However, 15 per...
 3.3.17: In a certain community, 36 percent of the familiesown a dog and 22 ...
 3.3.18: A total of 46 percent of the voters in a certain cityclassify thems...
 3.3.19: A total of 48 percent of the women and 37 percentof the men that to...
 3.3.20: Fiftytwo percent of the students at a certain collegeare females. ...
 3.3.21: A total of 500 married working couples werepolled about their annua...
 3.3.22: A red die, a blue die, and a yellow die (all sixsided) are rolled. ...
 3.3.23: Urn I contains 2 white and 4 red balls, whereas urnII contains 1 wh...
 3.3.24: Each of 2 balls is painted either black or gold andthen placed in a...
 3.3.25: The following method was proposed to estimatethe number of people o...
 3.3.26: Suppose that 5 percent of men and .25 percentof women are color bli...
 3.3.27: All the workers at a certain company drive towork and park in the c...
 3.3.28: Suppose that an ordinary deck of 52 cards is shuffledand the cards ...
 3.3.29: There are 15 tennis balls in a box, of which 9 havenot previously b...
 3.3.30: Consider two boxes, one containing 1 black and 1white marble, the o...
 3.3.31: Ms. Aquina has just had a biopsy on a possibly canceroustumor. Not ...
 3.3.32: A family has j children with probability pj, wherep1 = .1, p2 = .25...
 3.3.33: On rainy days, Joe is late to work with probability.3; on nonrainy ...
 3.3.34: In Example 3f, suppose that the new evidence issubject to different...
 3.3.35: With probability .6, the present was hidden bymom; with probability...
 3.3.36: Stores A, B, and C have 50, 75, and 100 employees,respectively, and...
 3.3.37: (a) A gambler has a fair coin and a twoheadedcoin in his pocket. H...
 3.3.38: Urn A has 5 white and 7 black balls. Urn B has3 white and 12 black ...
 3.3.39: In Example 3a, what is the probability that someonehas an accident ...
 3.3.40: Consider a sample of size 3 drawn in the followingmanner: We start ...
 3.3.41: A deck of cards is shuffled and then divided intotwo halves of 26 c...
 3.3.42: Three cooks, A, B, and C, bake a special kind ofcake, and with resp...
 3.3.43: There are 3 coins in a box. One is a twoheadedcoin, another is a f...
 3.3.44: Three prisoners are informed by their jailer thatone of them has be...
 3.3.45: Suppose we have 10 coins such that if the ithcoin is flipped, heads...
 3.3.46: In any given year, a male automobile policyholderwill make a claim ...
 3.3.47: An urn contains 5 white and 10 black balls. A fairdie is rolled and...
 3.3.48: Each of 2 cabinets identical in appearance has 2drawers. Cabinet A ...
 3.3.49: Prostate cancer is the most common type of cancerfound in males. As...
 3.3.50: Suppose that an insurance company classifies peopleinto one of thre...
 3.3.51: A worker has asked her supervisor for a letter ofrecommendation for...
 3.3.52: A high school student is anxiously waiting toreceive mail telling h...
 3.3.53: A parallel system functions whenever at least oneof its components ...
 3.3.54: If you had to construct a mathematical model forevents E and F, as ...
 3.3.55: In a class, there are 4 freshman boys, 6 freshmangirls, and 6 sopho...
 3.3.56: Suppose that you continually collect coupons andthat there are m di...
 3.3.57: A simplified model for the movement of the priceof a stock supposes...
 3.3.58: Suppose that we want to generate the outcomeof the flip of a fair c...
 3.3.59: Independent flips of a coin that lands on headswith probability p a...
 3.3.60: The color of a persons eyes is determined by a singlepair of genes....
 3.3.61: Genes relating to albinism are denoted by A anda. Only those people...
 3.3.62: Barbara and Dianne go target shooting. Supposethat each of Barbaras...
 3.3.63: A and B are involved in a duel. The rules of theduel are that they ...
 3.3.64: A truefalse question is to be posed to a husbandandwife team on a ...
 3.3.65: In 3.5, if p = .6 and the couple uses thestrategy in part (b), what...
 3.3.66: The probability of the closing of the ith relay in thecircuits show...
 3.3.67: An engineering system consisting of n componentsis said to be a ko...
 3.3.68: In 3.65a, find the conditional probabilitythat relays 1 and 2 are b...
 3.3.69: A certain organism possesses a pair of each of 5different genes (wh...
 3.3.70: There is a 5050 chance that the queen carries thegene for hemophili...
 3.3.71: On the morning of September 30, 1982, the wonlost records of the th...
 3.3.72: A town council of 7 members contains a steeringcommittee of size 3....
 3.3.73: Suppose that each child born to a couple is equallylikely to be a b...
 3.3.74: A and B alternate rolling a pair of dice, stoppingeither when A rol...
 3.3.75: In a certain village, it is traditional for the eldestson (or the o...
 3.3.76: Suppose that E and F are mutually exclusiveevents of an experiment....
 3.3.77: Consider an unending sequence of independenttrials, where each tria...
 3.3.78: A and B play a series of games. Each game is independentlywon by A ...
 3.3.79: In successive rolls of a pair of fair dice, what is theprobability ...
 3.3.80: In a certain contest, the players are of equal skilland the probabi...
 3.3.81: An investor owns shares in a stock whose presentvalue is 25. She ha...
 3.3.82: A and B flip coins. A starts and continues flippinguntil a tail occ...
 3.3.83: Die A has 4 red and 2 white faces, whereas die Bhas 2 red and 4 whi...
 3.3.84: An urn contains 12 balls, of which 4 are white.Three playersA, B, a...
 3.3.85: Repeat 3.84 when each of the 3 playersselects from his own urn. Tha...
 3.3.86: Let S = {1, 2, . . . , n} and suppose that A and B are,independentl...
 3.3.87: In Example 5e, what is the conditional probabilitythat the ith coin...
 3.3.88: In Laplaces rule of succession (Example 5e), arethe outcomes of the...
 3.3.89: A person tried by a 3judge panel is declared guiltyif at least 2 j...
 3.3.90: Suppose that n independent trials, each of whichresults in any of t...
Solutions for Chapter 3: First Course in Probability 8th Edition
Full solutions for First Course in Probability  8th Edition
ISBN: 9780136033134
Solutions for Chapter 3
Get Full SolutionsChapter 3 includes 90 full stepbystep solutions. This textbook survival guide was created for the textbook: First Course in Probability, edition: 8. Since 90 problems in chapter 3 have been answered, more than 2903 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. First Course in Probability was written by Sieva Kozinsky and is associated to the ISBN: 9780136033134.

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Average
See Arithmetic mean.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Central tendency
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

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.

Counting techniques
Formulas used to determine the number of elements in sample spaces and events.

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Demingâ€™s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Error variance
The variance of an error term or component in a model.

Estimate (or point estimate)
The numerical value of a point estimator.

Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

Event
A subset of a sample space.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Fraction defective
In statistical quality control, that portion of a number of units or the output of a process that is defective.

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.

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

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

Generator
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
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