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AlgebraAlgebra and Trigonometry (MindTap Course List)(a) What is meant by the conditional probability of E given F ? How is this probability calculated? (b) What are independent events? (c) If E and F are independent events, what is the probability of E and F occurring? What if E and F are not independent? (d) A jar contains 3 white and 7 black balls. Let E be the event “the first ball drawn is black” and let F be the event “the second ball drawn is black.” (i) Find P ( E ∩ F ) if the balls are drawn with replacement. (ii) Find P ( E ∩ F ) if the balls are drawn without replacement.BuyFind*arrow_forward*

4th Edition

James Stewart + 2 others

Publisher: Cengage Learning

ISBN: 9781305071742

Chapter 14.CR, Problem 7CC

Textbook Problem

**(a)** What is meant by the conditional probability of *E* given *F*? How is this probability calculated?

**(b)** What are independent events?

**(c)** If *E* and *F* are independent events, what is the probability of *E* and *F* occurring? What if *E* and *F* are not independent?

**(d)** A jar contains 3 white and 7 black balls. Let *E* be the event “the first ball drawn is black” and let *F* be the event “the second ball drawn is black.”

**(i)** Find

**(ii)** Find

Algebra and Trigonometry (MindTap Course List)

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Ch. 14.1 - CONCEPTS The Fundamental Counting Principle says...Ch. 14.1 - CONCEPTS The number of ways of arranging r objects...Ch. 14.1 - CONCEPTS The number of ways of choosing r objects...Ch. 14.1 - CONCEPTS True or False? aIn counting combinations,...Ch. 14.1 - SKILLS 5-16 Evaluating Permutations and...Ch. 14.1 - SKILLS 5-16 Evaluating Permutations and...Ch. 14.1 - SKILLS 5-16 Evaluating Permutations and...Ch. 14.1 - SKILLS 5-16 Evaluating Permutations and...Ch. 14.1 - SKILLS 5-16 Evaluating Permutations and...Ch. 14.1 - SKILLS 5-16 Evaluating Permutations and...

Ch. 14.1 - 5-6 Evaluating Permutations and Combinations...Ch. 14.1 - 5-6 Evaluating Permutations and Combinations...Ch. 14.1 - 5-6 Evaluating Permutations and Combinations...Ch. 14.1 - 5-6 Evaluating Permutations and Combinations...Ch. 14.1 - 5-6 Evaluating Permutations and Combinations...Ch. 14.1 - 5-6 Evaluating Permutations and Combinations...Ch. 14.1 - 17-36Fundamental Counting Principal These...Ch. 14.1 - 17-36 Fundamental Counting Principle These...Ch. 14.1 - 17-36 Fundamental Counting Principle These...Ch. 14.1 - Multiple-Choice TestA multiple-choice test has...Ch. 14.1 - Phone NumbersTelephone numbers consist of seven...Ch. 14.1 - Running a RaceIn how many different ways can a...Ch. 14.1 - Restaurant MealsA restaurant offers the items...Ch. 14.1 - Multiple RoutesTowns A, B, C, and D are located in...Ch. 14.1 - Flipping a CoinA coin is flipped five times, and...Ch. 14.1 - Rolling a Pair of Dice A red die and a white die...Ch. 14.1 - Rolling Three Dice A red die, a blue die, and a...Ch. 14.1 - Choosing Outfits A girl has five skirts, eight...Ch. 14.1 - License Plate Standard automobile license plates...Ch. 14.1 - ID Numbers A companys employee ID number system...Ch. 14.1 - APPLICATIONS 17-36 Fundamental Counting...Ch. 14.1 - APPLICATIONS 17-36 Fundamental Counting...Ch. 14.1 - APPLICATIONS 17-36 Fundamental Counting...Ch. 14.1 - APPLICATIONS 17-36 Fundamental Counting...Ch. 14.1 - APPLICATIONS 17-36 Fundamental Counting...Ch. 14.1 - APPLICATIONS 17-36 Fundamental Counting...Ch. 14.1 - APPLICATIONS 37-40 Counting Subsets These...Ch. 14.1 - APPLICATIONS 37-40 Counting Subsets These...Ch. 14.1 - APPLICATIONS 37-40 Counting Subsets These...Ch. 14.1 - APPLICATIONS 37-40 Counting Subsets These...Ch. 14.1 - 4152Counting PermutationsThese exercises involves...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 41-52 Counting Permutations These exercises...Ch. 14.1 - 53-56 Distinguishable Permutations These exercises...Ch. 14.1 - 53-56 Distinguishable Permutations These exercises...Ch. 14.1 - 53-56 Distinguishable Permutations These exercises...Ch. 14.1 - 53-56 Distinguishable Permutations These exercises...Ch. 14.1 - Distributions A man bought three vanilla ice-cream...Ch. 14.1 - Room Assignments When seven students take a trip,...Ch. 14.1 - Work Assignments Eight workers are cleaning a...Ch. 14.1 - Transporting Students A group of 30 students is...Ch. 14.1 - 61-74CombinationsThese exercises involve counting...Ch. 14.1 - 61-74CombinationsThese exercises involve counting...Ch. 14.1 - 61-74CombinationsThese exercises involve counting...Ch. 14.1 - 61-74CombinationsThese exercises involve counting...Ch. 14.1 - 61-74CombinationsThese exercises involve counting...Ch. 14.1 - 61-74CombinationsThese exercises involve counting...Ch. 14.1 - 61-74CombinationsThese exercises involve counting...Ch. 14.1 - APPLICATIONS 61-74 CombinationsThese exercises...Ch. 14.1 - APPLICATIONS 61-74 CombinationsThese exercises...Ch. 14.1 - APPLICATIONS 61-74 CombinationsThese exercises...Ch. 14.1 - APPLICATIONS 61-74 CombinationsThese exercises...Ch. 14.1 - APPLICATIONS 61-74 CombinationsThese exercises...Ch. 14.1 - APPLICATIONS 61-74 CombinationsThese exercises...Ch. 14.1 - APPLICATIONS 61-74 CombinationsThese exercises...Ch. 14.1 - APPLICATIONS 75-90 Counting PrinciplesSolve these...Ch. 14.1 - APPLICATIONS 75-90 Counting PrinciplesSolve these...Ch. 14.1 - APPLICATIONS 75-90 Counting PrinciplesSolve these...Ch. 14.1 - APPLICATIONS 75-90 Counting PrinciplesSolve these...Ch. 14.1 - Dance Committee A school dance committee is to...Ch. 14.1 - Casting a Play A group of 22 aspiring thespians...Ch. 14.1 - Hockey Lineup A hockey team has 20 players, of...Ch. 14.1 - Choosing a Pizza A pizza parlour offers four sizes...Ch. 14.1 - Choosing a Committee In how many ways can a...Ch. 14.1 - Parking Committee A five person committee...Ch. 14.1 - Arranging Books In how many ways can five...Ch. 14.1 - Arranging a Class PictureIn how many ways can ten...Ch. 14.1 - Seating ArrangementsIn how many ways can four men...Ch. 14.1 - Seating ArrangementsIn how many ways can four men...Ch. 14.1 - Selecting Prizewinners From a group of 30...Ch. 14.1 - Choosing a Delegation Three delegates are to be...Ch. 14.1 - DISCUSS: Pair of InitialsExplain why in any group...Ch. 14.1 - DISCUSS:Complementary CombinationsWithout...Ch. 14.1 - DISCUSS:An Identity Involving CombinationsKelvin...Ch. 14.1 - DISCUSS DISCOVER: Why Is (nr)the Same as...Ch. 14.2 - The set of all possible outcomes of an experiment...Ch. 14.2 - Let E and F be events in a sample space S. aThe...Ch. 14.2 - The conditional probability of E given that F...Ch. 14.2 - Let E and F be events in a sample space S. aThe...Ch. 14.2 - Rolling a Die An experiment consists of rolling a...Ch. 14.2 - Tossing a coin An experiment consists of tossing a...Ch. 14.2 - 720 Probability by Counting These exercises...Ch. 14.2 - 720 Probability by Counting These exercises...Ch. 14.2 - 9-10 A die is rolled. Find the probability of the...Ch. 14.2 - 9-10 A die is rolled. Find the probability of the...Ch. 14.2 - 1112 A card is drawn randomly from a standard...Ch. 14.2 - 1112 A card is drawn randomly from a standard...Ch. 14.2 - 1314 A ball is drawn randomly from a jar that...Ch. 14.2 - 1314 A ball is drawn randomly from a jar that...Ch. 14.2 - A poker hand, consisting of five cards, is dealt...Ch. 14.2 - Three CDs are picked at random from a collection...Ch. 14.2 - Two balls are picked at random from a jar that...Ch. 14.2 - A letter is chosen at random from the word...Ch. 14.2 - A five-card poker hand is drawn from a standard...Ch. 14.2 - A pair of dice is rolled, and the numbers showing...Ch. 14.2 - Union of EventsThese exercises involve finding the...Ch. 14.2 - Union of EventsThese exercises involve finding the...Ch. 14.2 - A die is rolled, and the number showing is...Ch. 14.2 - A die is rolled, and the number showing is...Ch. 14.2 - 25-26 A card is drawn at random from a standard 52...Ch. 14.2 - 25-26 A card is drawn at random from a standard 52...Ch. 14.2 - 27-32 Conditional ProbabilityThese exercises...Ch. 14.2 - 27-32 Conditional ProbabilityThese exercises...Ch. 14.2 - 29-30 Refer to the spinner in Exercises 2122. Find...Ch. 14.2 - 29-30 Refer to the spinner in Exercises 2122. Find...Ch. 14.2 - 31-32 A jar contains five red balls numbered 1 to...Ch. 14.2 - 31-32 A jar contains five red balls numbered 1 to...Ch. 14.2 - 33-40 Intersection of Events These exercises...Ch. 14.2 - 33-40 Intersection of Events These exercises...Ch. 14.2 - 33-40 Intersection of Events These exercises...Ch. 14.2 - 33-40 Intersection of Events These exercises...Ch. 14.2 - 33-40 Intersection of Events These exercises...Ch. 14.2 - 33-40 Intersection of Events These exercises...Ch. 14.2 - 39-40 Spinners A and B shown in the figure are...Ch. 14.2 - 39-40 Spinners A and B shown in the figure are...Ch. 14.2 - Four Siblings A couple intends to have four...Ch. 14.2 - Bridge Hands What is the probability that a...Ch. 14.2 - Roulette An American roulette wheel has 38 slots....Ch. 14.2 - Making Words A toddler has wooden blocks showing...Ch. 14.2 - Lottery In the 6/49 lottery game, a player selects...Ch. 14.2 - An unlikely event The president of a large company...Ch. 14.2 - Guessing on a test An exam has ten true-false...Ch. 14.2 - Quality Control To control the quality of their...Ch. 14.2 - Monkeys Typing Shakespeare An often-quoted example...Ch. 14.2 - Making Words A monkey is trained to arrange wooden...Ch. 14.2 - APPLICATIONS Making Words A toddler has eight...Ch. 14.2 - APPLICATIONS Horse Race Eight horses are entered...Ch. 14.2 - APPLICATIONS Genetics Many genetic traits are...Ch. 14.2 - APPLICATIONS Genetics Refer to Exercise 53. Make a...Ch. 14.2 - APPLICATIONS Roulette An American roulette wheel...Ch. 14.2 - APPLICATIONS Choosing a Committee A committee of...Ch. 14.2 - APPLICATIONS Snake eyes What is the probability of...Ch. 14.2 - APPLICATIONS Lottery In the 6/49 lottery game a...Ch. 14.2 - APPLICATIONS Marbles In a Jar A jar contains six...Ch. 14.2 - APPLICATIONS LotteryIn the 6/49 lottery game, a...Ch. 14.2 - APPLICATIONS Balls in a JarJar A contains three...Ch. 14.2 - APPLICATIONS Slot Machine A slot machine has three...Ch. 14.2 - APPLICATIONS Combination Lock A student has locked...Ch. 14.2 - APPLICATIONS Committee Membership A mathematics...Ch. 14.2 - APPLICATIONS Class Photo Twenty students are...Ch. 14.2 - APPLICATIONS Making Words A monkey is trained to...Ch. 14.2 - APPLICATIONS Making WordsA monkey is trained to...Ch. 14.2 - DISCUSS:Oldest SonA family with two children is...Ch. 14.3 - CONCEPTS A binomial experiment is one in which...Ch. 14.3 - CONCEPTS If a binomial experiment has probability...Ch. 14.3 - SKILLS 3-14Binomial Trials Five independent trials...Ch. 14.3 - SKILLS 3-14Binomial Trials Five independent trials...Ch. 14.3 - SKILLS 3-14Binomial Trials Five independent trials...Ch. 14.3 - SKILLS 3-14Binomial Trials Five independent trials...Ch. 14.3 - SKILLS 3-14Binomial Trials Five independent trials...Ch. 14.3 - SKILLS 3-14Binomial Trials Five independent trials...Ch. 14.3 - SKILLS 3-14Binomial Trials Five independent trials...Ch. 14.3 - SKILLS 3-14Binomial Trials Five independent trials...Ch. 14.3 - SKILLS 3-14 Binomial Trials Five independent...Ch. 14.3 - SKILLS 3-14 Binomial Trials Five independent...Ch. 14.3 - SKILLS 3-14 Binomial Trials Five independent...Ch. 14.3 - SKILLS 3-14 Binomial Trials Five independent...Ch. 14.3 - SKILLS 15-16 Probability Distribution An...Ch. 14.3 - SKILLS 15-16 Probability Distribution An...Ch. 14.3 - SKILLS 17-20 Probability Distribution A binomial...Ch. 14.3 - SKILLS 17-20 Probability Distribution A binomial...Ch. 14.3 - SKILLS 17-20 Probability Distribution A binomial...Ch. 14.3 - SKILLS 17-20 Probability Distribution A binomial...Ch. 14.3 - Rolling DiceSix dice are rolled. Find the...Ch. 14.3 - ArcheryAn archer hits his target 80 of the time....Ch. 14.3 - Television RatingsAccording to a ratings survey,...Ch. 14.3 - Spread of DiseaseHealth authorities estimate that...Ch. 14.3 - Blood TypeAbout 45 of the populations of the...Ch. 14.3 - HandednessA psychologist needs 12 left-handed...Ch. 14.3 - Germination RatesA certain brand of tomato seeds...Ch. 14.3 - Genders of ChildrenAssume that for any given line...Ch. 14.3 - Genders of ChildrenThe ratio of male to female...Ch. 14.3 - Education LevelIn a certain county 20 of the...Ch. 14.3 - Defective Light Bulbs The Dim Bulb Lighting...Ch. 14.3 - Quality Control An assembly line that manufactures...Ch. 14.3 - Sick Leave The probability that a given worker at...Ch. 14.3 - Political Surveys In a certain county, 60 of the...Ch. 14.3 - Pharmaceuticals A drug that is used to prevent...Ch. 14.3 - Reliability of a Machine A machine that is used in...Ch. 14.3 - Genetics Huntingtons disease is a hereditary...Ch. 14.3 - Selecting CardsThree cards are randomly selected...Ch. 14.3 - Smokers and Nonsmokers The participants at a...Ch. 14.3 - Telephone Marketing A mortgage company advertises...Ch. 14.3 - Effectiveness of a Drug A certain disease has a...Ch. 14.3 - Hitting a Target An archer normally hits the...Ch. 14.3 - DISCUSS: Most Likely Outcome for nTosses of a Coin...Ch. 14.4 - CONCEPTS 1. If a game gives payoffs of 10 and 100...Ch. 14.4 - CONCEPTS If you played the game in Exercise 1 many...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - SKILLS 3-12 Expected Value of a Game Find the...Ch. 14.4 - APPLICATIONS Roulette An American roulette wheel...Ch. 14.4 - APPLICATIONS Sweepstakes A sweepstakes offers a...Ch. 14.4 - APPLICATIONS A Game of Chance A box contains 100...Ch. 14.4 - APPLICATIONS Combination Lock A safe containing...Ch. 14.4 - APPLICATIONS Gambling on Stocks An investor buys...Ch. 14.4 - APPLICATIONS Slot Machine A slot machine has three...Ch. 14.4 - APPLICATIONS Lottery In a 6/49 lottery game, a...Ch. 14.4 - APPLICATIONS Lightning Insurance An insurance...Ch. 14.4 - APPLICATION Expected Number During the school year...Ch. 14.4 - APPLICATION Expected Number In a large liberal...Ch. 14.4 - APPLICATION Expected Number A student goes to swim...Ch. 14.4 - APPLICATION Expected Number Consider families with...Ch. 14.4 - APPLICATION 25-30 A fair Game? A game of chance...Ch. 14.4 - APPLICATIONS 25-30 A Fair Game? A game of chance...Ch. 14.4 - 25-30 A Fair Game? A game of chance is described....Ch. 14.4 - 25-30 A Fair Game? A game of chance is described....Ch. 14.4 - APPLICATIONS 25-30 A Fair Game?A game of chance...Ch. 14.4 - APPLICATIONS 25-30 A Fair Game?A game of chance...Ch. 14.4 - DISCUSSDISCOVERPROVEWRITE DISCUSS: The Expected...Ch. 14.CR - a What does the Fundamental Counting Principle...Ch. 14.CR - a What is a permutation of r elements of a set?...Ch. 14.CR - a What is a combination of r elements of a set?...Ch. 14.CR - a In solving a problem involving picking r objects...Ch. 14.CR - a What is meant by an experiment? Sample space? b...Ch. 14.CR - a What are mutually exclusive events? b If E and F...Ch. 14.CR - a What is meant by the conditional probability of...Ch. 14.CR - a An experiment has two outcomes, success and...Ch. 14.CR - a Suppose that a game gives payouts a1,a2,...,an...Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - 1-24 Counting These exercises involve counting....Ch. 14.CR - Probability These exercises involve probability....Ch. 14.CR - Marbles in a Jar If two marbles are drawn from the...Ch. 14.CR - Coin Toss A coin is tossed three times in a row,...Ch. 14.CR - Choosing Books A shelf has ten books: two...Ch. 14.CR - Rolling a Die and Selecting a Card A die is...Ch. 14.CR - Selecting Cards Find the probability that the...Ch. 14.CR - Rolling a Die, Selecting a Card, and tossing a...Ch. 14.CR - Rolling Dice Two dice are rolled. Find the...Ch. 14.CR - Selecting a Card Four cards are dealt from a...Ch. 14.CR - Lottery In the numbers game lottery a player picks...Ch. 14.CR - Game Show In a TV game show, a contestant is given...Ch. 14.CR - 25-42 ProbabilityThese exercises involve...Ch. 14.CR - 25-42 ProbabilityThese exercises involve...Ch. 14.CR - 25-42 ProbabilityThese exercises involve...Ch. 14.CR - 25-42 ProbabilityThese exercises involve...Ch. 14.CR - 25-42 ProbabilityThese exercises involve...Ch. 14.CR - 25-42 ProbabilityThese exercises involve...Ch. 14.CR - 25-42 ProbabilityThese exercises involve...Ch. 14.CR - 43-46 Binomial ProbabilityThese exercises involve...Ch. 14.CR - 43-46 Binomial ProbabilityThese exercises involve...Ch. 14.CR - 43-46 Binomial ProbabilityThese exercises involve...Ch. 14.CR - 43-46 Binomial ProbabilityThese exercises involve...Ch. 14.CR - 47-50Expected ValueThese exercises involve...Ch. 14.CR - 47-50Expected ValueThese exercises involve...Ch. 14.CR - 47-50Expected ValueThese exercises involve...Ch. 14.CR - 47-50Expected ValueThese exercises involve...Ch. 14.CT - Alice and Bill have four grandchildren, and they...Ch. 14.CT - A hospital cafeteria offers a fixed-price lunch...Ch. 14.CT - An Internet service provider requires its customer...Ch. 14.CT - Over the past year, John has purchased 30 books. a...Ch. 14.CT - A commuter must travel from Ajax to Barrie and...Ch. 14.CT - A pizza parlor offers four sizes of pizza and 14...Ch. 14.CT - An anagram of a word is a rearrangement of the...Ch. 14.CT - A board of directors consisting of eight members...Ch. 14.CT - One card is drawn from a deck. Find the...Ch. 14.CT - A jar contains five red balls, numbered 1 to 5,...Ch. 14.CT - Three people are chosen at random from a group of...Ch. 14.CT - 12. Two dice are rolled. What is the probability...Ch. 14.CT - 13. In a group of four students, what is the...Ch. 14.CT - An unbalanced coin weighted so that the...Ch. 14.CT - You are to draw one card from a deck. If it is an...Ch. 14.FOM - 1. Winning Strategy In a game show like the one...Ch. 14.FOM - Family PlanningA couple intends to have two...Ch. 14.FOM - Dividing a JackpotA game between two players...Ch. 14.FOM - Estimating In this problem we use the Monte Carlo...Ch. 14.FOM - Areas of Curved Regions The Monte Carlo method can...Ch. 14.FOM - Random NumbersChoose two numbers at random from...

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