Explanation We have given that, P ( A ∩ B C ) = 0.3 P ( A ∪ B ) C = 0.2 P ( A ∩ B ) = 0.1 P ( A ∩ B C ) = P ( A ) − P ( A ∩ B ) 0.3 = P ( A ) − 0.1 P ( A ) = 0.4 P ( A ∪ B ) C = 1 − P ( A ∪ B ) P ( A ∪ B ) = 1 − P ( A ∪ B ) C P ( A ∪ B ) = 1 − 0.2 P ( A ∪ B ) = 0

An Introduction to Mathematical Statistics and Its Applications (6th Edition)

6th Edition

ISBN: 9780134114217

Author: Richard J. Larsen, Morris L. Marx

Publisher: PEARSON

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Chapter 2.4, Problem 15Q

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To find: P(A|B).

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Chapter 2.4, Problem 14Q

Chapter 2.4, Problem 16Q

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If P (A) =0.45, P (B) =0.7, and P (A and B) = 0.4, find P (A or B).

Let P (A) = 0.4 and P (A ∪ B) = 0.6. For what value of P (B) are A and B independent?

If P(B) = 0.30, P(A ∪ B) = 0.65, and P(A ∩ B) = 0.15, find P(A).

Chapter 2 Solutions

An Introduction to Mathematical Statistics and Its Applications (6th Edition)

Ch. 2.2 - A graduating engineer has signed up for three job...Ch. 2.2 - Three dice are tossed, one red, one blue, and one...Ch. 2.2 - An urn contains six chips numbered 1 through 6....Ch. 2.2 - Suppose that two cards are dealt from a standard...Ch. 2.2 - In the lingo of craps-shooters (where two dice are...Ch. 2.2 - A poker deck consists of fifty-two cards,...Ch. 2.2 - Let P be the set of right triangles with a 5...Ch. 2.2 - Suppose a baseball player steps to the plate with...Ch. 2.2 - A telemarketer is planning to set up a phone bank...Ch. 2.2 - Two darts are thrown at the following target: (a)...

Ch. 2.2 - A woman has her purse snatched by two teenagers....Ch. 2.2 - Consider the experiment of choosing coefficients...Ch. 2.2 - In the game of craps, the person rolling the dice...Ch. 2.2 - A probability-minded despot offers a convicted...Ch. 2.2 - Suppose that ten chips, numbered 1 through 10, are...Ch. 2.2 - Sketch the regions in the xy-plane corresponding...Ch. 2.2 - Referring to Example 2.2.7, find (AB) and (AB) if...Ch. 2.2 - Find (ABC) if A={x:0x4}, B={x:2x6} and...Ch. 2.2 - Prob. 19Q Ch. 2.2 - Prob. 20Q Ch. 2.2 - Let A be the set of five-card hands dealt from a...Ch. 2.2 - Suppose that each of the twelve letters in the...Ch. 2.2 - Let A, B, and C be any three events defined on a...Ch. 2.2 - Let A1,A2,........,Ak be any set of events defined...Ch. 2.2 - Let A, B, and C be any three events defined on a...Ch. 2.2 - Suppose that three eventsA, B, and Care de-fined...Ch. 2.2 - Prob. 27Q Ch. 2.2 - Let events A and B and sample space S be defined...Ch. 2.2 - A coin is tossed four times and the resulting...Ch. 2.2 - Pictured below are two organizational charts...Ch. 2.2 - During orientation week, the latest Spiderman...Ch. 2.2 - Let A and B be any two events. Use Venn diagrams...Ch. 2.2 - Let A, B, and C be any three events. Use Venn...Ch. 2.2 - Let A, B, and C be any three events. Use Venn...Ch. 2.2 - Let A and B be any two events defined on a sample...Ch. 2.2 - Use Venn diagrams to suggest an equivalent way of...Ch. 2.2 - A total of twelve hundred graduates of State Tech...Ch. 2.2 - Let A, B, and C be any three events defined on a...Ch. 2.2 - A poll conducted by a potential presidential...Ch. 2.2 - For two events A and B defined on a sample space...Ch. 2.3 - According to a family-oriented lobbying group,...Ch. 2.3 - Let A and B be any two events defined on S....Ch. 2.3 - Express the following probabilities in terms of...Ch. 2.3 - LetAandBbe two events defined on S. If the...Ch. 2.3 - Suppose that three fair dice are tossed. Let Ai be...Ch. 2.3 - Events A and B are defined on a sample space S...Ch. 2.3 - Let A1,A2....,An be a series of events for which...Ch. 2.3 - Draw the Venn diagrams that would correspond to...Ch. 2.3 - In the game of odd man out each player tosses a...Ch. 2.3 - An urn contains twenty-four chips, numbered 1...Ch. 2.3 - If States football team has a 10% chance of...Ch. 2.3 - Let events A1 and A2 are such that A1A2=S and...Ch. 2.3 - Prob. 13Q Ch. 2.3 - Prob. 14Q Ch. 2.3 - A coin is to be tossed four times. Define events X...Ch. 2.3 - Two dice are tossed. Assume that each possible...Ch. 2.3 - Let A, B, and C be three events defined on a...Ch. 2.3 - Lucy is currently running two dot-com scams out of...Ch. 2.4 - Suppose that two fair dice are tossed. What is the...Ch. 2.4 - Find P(AB) if P(A)=0.2,P(B)=0.4, and...Ch. 2.4 - If P(AB)P(A), show that P(BA)P(B).Ch. 2.4 - Let A and B be two events such that...Ch. 2.4 - Suppose that in Example 2.4.2 we ignored the ages...Ch. 2.4 - Two events, A and B, are defined on a sample space...Ch. 2.4 - An urn contains one red chip and one white chip....Ch. 2.4 - Given that P(A)=a and P(B)=b, show that P(AB)a+b1b Ch. 2.4 - An urn contains one white chip and a second chip...Ch. 2.4 - Suppose events A and B are such that P(AB)=0.1 and...Ch. 2.4 - One hundred voters were asked their opinions of...Ch. 2.4 - A fair coin is tossed three times. What is the...Ch. 2.4 - Two fair dice are rolled. What is the probability...Ch. 2.4 - Four cards are dealt from a standard 52-card poker...Ch. 2.4 - Prob. 15Q Ch. 2.4 - Given that P(A)+P(B)=0.9,P(AB)=0.5, and...Ch. 2.4 - Let A and B be two events defined on a sample...Ch. 2.4 - Suppose two dice are rolled. Assume that each...Ch. 2.4 - According to your neighborhood bookie, five horses...Ch. 2.4 - Andy, Bob, and Charley have all been serving time...Ch. 2.4 - An urn contains six white chips, four black chips,...Ch. 2.4 - A man has n keys on a key ring, one of which opens...Ch. 2.4 - Your favorite college football team has had a good...Ch. 2.4 - One chip is drawn at random from an urn that...Ch. 2.4 - A toy manufacturer buys ball bearings from three...Ch. 2.4 - A fair coin is tossed. 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The first contains two...Ch. 2.4 - An automobile insurance company has compiled the...Ch. 2.5 - Suppose that P(AB)=0.2, P(A)=0.6, and P(B)=0.5....Ch. 2.5 - Spike is not a terribly bright student. His...Ch. 2.5 - Two fair dice are rolled. What is the probability...Ch. 2.5 - Emma and Josh have just gotten engaged. What is...Ch. 2.5 - Dana and Cathy are playing tennis. The probability...Ch. 2.5 - Three points, X1,X2andX3, are chosen at random in...Ch. 2.5 - Suppose that P(A)=14andP(B)=18 (a) What does P(AB)...Ch. 2.5 - Suppose that events A, B, and C are independent....Ch. 2.5 - A fair coin is tossed four times. 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The...Ch. 2.5 - Prob. 21Q Ch. 2.5 - According to an advertising study, 15% of...Ch. 2.5 - A fair die is rolled and then n fair coins are...Ch. 2.5 - Prob. 24Q Ch. 2.5 - If two fair dice are tossed, what is the smallest...Ch. 2.5 - Prob. 26Q Ch. 2.5 - An urn contains w white chips, b black chips, and...Ch. 2.5 - Prob. 28Q Ch. 2.5 - A computer is instructed to generate a random...Ch. 2.5 - Prob. 30Q Ch. 2.5 - Stanleys statistics seminar is graded on a...Ch. 2.5 - What is the smallest number of switches wired in...Ch. 2.6 - Achemical engineer wishes to observe the effects...Ch. 2.6 - A coded message from a CIA operative to his...Ch. 2.6 - How many terms will be included in the expansion...Ch. 2.6 - Suppose that the format for license plates in a...Ch. 2.6 - How many integers between 100 and 999 have...Ch. 2.6 - A fast-food restaurant offers customers a choice...Ch. 2.6 - In baseball there are twenty-four different...Ch. 2.6 - Recall the postal zip codes described in Example...Ch. 2.6 - Arestaurant offers a choice of four appetizers,...Ch. 2.6 - An octave contains twelve distinct notes (on a...Ch. 2.6 - Residents of a condominium have an automatic...Ch. 2.6 - In international Morse code, each letter in the...Ch. 2.6 - The decimal number corresponding to a sequence of...Ch. 2.6 - Given the letters in the word ZOMBIESin how many...Ch. 2.6 - Suppose that two cards are drawnin orderfrom a...Ch. 2.6 - Monicas vacation plans require that she fly from...Ch. 2.6 - The board of a large corporation has six members...Ch. 2.6 - How many ways can a set of four tires be put on a...Ch. 2.6 - Use Stirlings formula to approximate 30!.(Note:...Ch. 2.6 - The nine members of the music faculty baseball...Ch. 2.6 - A three-digit number is to be formed from the...Ch. 2.6 - Four men and four women are to be seated in a row...Ch. 2.6 - An engineer needs to take three technical...Ch. 2.6 - How many ways can a twelve-member cheerleading...Ch. 2.6 - Suppose that a seemingly interminable German opera...Ch. 2.6 - A new horror movie, Friday the 13th, Part X, will...Ch. 2.6 - Suppose that ten people, including you and a...Ch. 2.6 - Use an induction argument to prove Theo-rem 2.6.1....Ch. 2.6 - In how many ways can a pack of fifty-two cards be...Ch. 2.6 - If the definition of n! is to hold for all...Ch. 2.6 - The crew of Apollo 17 consisted of a pilot, a...Ch. 2.6 - Uncle Harry and Aunt Minnie will both be attending...Ch. 2.6 - In how many ways can the digits 1 through 9 be...Ch. 2.6 - Which state name can generate more permutations,...Ch. 2.6 - How many numbers greater than four million can...Ch. 2.6 - An interior decorator is trying to arrange a shelf...Ch. 2.6 - Four Nigerians (A, B, C, D), three Chinese (#, ,...Ch. 2.6 - How many ways can the letters in the word...Ch. 2.6 - A tennis tournament has a field of 2n entrants,...Ch. 2.6 - Prob. 40Q Ch. 2.6 - In how many ways can the letters of the word...Ch. 2.6 - In how many ways can the word ABRACADABRA be...Ch. 2.6 - Prob. 43Q Ch. 2.6 - Prob. 44Q Ch. 2.6 - Prob. 45Q Ch. 2.6 - Prob. 46Q Ch. 2.6 - In how many ways can the letters of the word...Ch. 2.6 - Prob. 48Q Ch. 2.6 - Prob. 49Q Ch. 2.6 - How many straight lines can be drawn between five...Ch. 2.6 - The Alpha Beta Zeta sorority is trying to fill a...Ch. 2.6 - A boat has a crew of eight: Two of those eight can...Ch. 2.6 - Nine students, five men and four women, interview...Ch. 2.6 - The final exam in History 101 consists of five...Ch. 2.6 - Ten basketball players meet in the school gym for...Ch. 2.6 - Your statistics teacher announces a twenty-page...Ch. 2.6 - In how many ways can the letters in MI S S I S S I...Ch. 2.6 - Prove that (kn+1)=(kn)+(k1n) directly without...Ch. 2.6 - Find a recursion formula for (k+1n) in terms of...Ch. 2.6 - Show that n(n1)2n2=k=2nk(k1)Cnk.Ch. 2.6 - Prob. 61Q Ch. 2.6 - Prob. 62Q Ch. 2.6 - Compare the coefficients of tk in...Ch. 2.7 - Ten equally qualified marketing assistants are...Ch. 2.7 - An urn contains six chips, numbered 1 through 6....Ch. 2.7 - Anurn contains twenty chips, numbered1 through 20....Ch. 2.7 - A bridge hand (thirteen cards) is dealt from a...Ch. 2.7 - Consider a set of ten urns, nine of which contain...Ch. 2.7 - A committee of fifty politicians is to be chosen...Ch. 2.7 - Suppose that n fair dice are rolled. 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P ( A | B ) .

Solution Summary: The author explains that P(A|B)=15 by definition of conditional probability.

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Chapter 2 Solutions