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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 8.5, Problem 91E

Textbook Problem

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**Drug Tests** If 90% of the athletes who test positive for steroids in fact use them, and 10% of all athletes use steroids and test positive, what percentage of athletes test positive?

To determine

**To calculate:** The percentage of athletes that test positive in the drug tests if there are 90% of the athletes who test positive for steroids and use them actually. There are 10% of all the athletes of all athletes use steroids and test positive.

**Given Information:**

There are 90% of the athletes who test positive for steroids and use them actually. There are 10% of all the athletes of all athletes use steroids and test positive.

**Formula used:**

If *A* and *B* are events with *A* given *B* is;

**Calculation:**

Consider the event that the athletes actually use steroids to be *A* and the event that the athletes test positive in the drug test to be *B*.

There are 10% of all the athletes of all athletes use steroids and test positive. This is represented by,

There are 90% of the athletes who test positive for steroids and use them actually.

This can be rewritten as the probability that an athlete actually uses steroids, given that the athlete tests positive in the drug test is

Finite Mathematics and Applied Calculus (MindTap Course List)

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Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - A packet of gummy candy contains four strawberry...Ch. 8.1 - A bag contains three red marbles, two blue ones,...Ch. 8.1 - President Barack H. 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An event is a...Ch. 8.1 - Complete the following sentence. Two events E and...Ch. 8.1 - If E and F are events, then (EF) is the event that...Ch. 8.1 - If E and F are events, then (EF) is the event that...Ch. 8.1 - Let E be the event that you meet a tall, dark...Ch. 8.1 - Let E be the event that you buy a Porsche. Which...Ch. 8.1 - True or false? Every set S is the sample space for...Ch. 8.1 - True or false? Every sample space S is a finite...Ch. 8.1 - Describe an experiment in which a die is cast and...Ch. 8.1 - Describe an experiment in which two coins are...Ch. 8.1 - Two distinguishable dice are rolled. 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She...Ch. 8.3 - Complete the following sentence. The probability...Ch. 8.3 - A friend of yours asserted at lunch today that,...Ch. 8.3 - A certain experiment is performed a large number...Ch. 8.3 - (Refer to Exercise 97.) 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Part A consists of...Ch. 8.4 - Tests A test has three parts. Part A consists of...Ch. 8.4 - Poker In Exercises 1924 you are asked to calculate...Ch. 8.4 - Poker In Exercises 1924 you are asked to calculate...Ch. 8.4 - Poker In Exercises 1924 you are asked to calculate...Ch. 8.4 - Poker In Exercises 1924 you are asked to calculate...Ch. 8.4 - Poker In Exercises 1924 you are asked to calculate...Ch. 8.4 - Poker In Exercises 1924 you are asked to calculate...Ch. 8.4 - The Monkey at the Typewriter Suppose that a monkey...Ch. 8.4 - The Cat on the Piano A standard piano keyboard has...Ch. 8.4 - (Based on a question from the GMAT) Tyler and...Ch. 8.4 - (Based on a question from the GMAT) Tyler and...Ch. 8.4 - Lotteries The Sorry State Lottery requires you to...Ch. 8.4 - Lotteries The Sad State Lottery requires you to...Ch. 8.4 - Transfers Your company is considering offering 400...Ch. 8.4 - Transfers (Refer back to Exercise 31.) After...Ch. 8.4 - Lotteries In a New York State daily lottery game,...Ch. 8.4 - Lotteries Refer back to Exercise 33. Find the...Ch. 8.4 - Elimination Tournaments In an elimination...Ch. 8.4 - Elimination Tournaments In a (fictitious) soccer...Ch. 8.4 - Elimination Tournaments The following diagram...Ch. 8.4 - Elimination Tournaments The following diagram...Ch. 8.4 - Elimination Tournaments The following diagram...Ch. 8.4 - Elimination Tournaments The following diagram...Ch. 8.4 - Sports The following table shows the results of...Ch. 8.4 - Sports Refer back to Exercise 41. Find the...Ch. 8.4 - Graph Searching A graph consists of a collection...Ch. 8.4 - Graph Searching Refer back to Exercise 43. Find...Ch. 8.4 - Product Design Your company has patented an...Ch. 8.4 - Product Design Assume that you already know the...Ch. 8.4 - Committees An investigatory committee in the...Ch. 8.4 - Committees A committee is to consist of a chair,...Ch. 8.4 - What is wrong with the following argument? A bag...Ch. 8.4 - What is wrong with the following argument? When we...Ch. 8.4 - Suzan grabs two marbles out of a bag of five red...Ch. 8.4 - If Suzan grabs two marbles, one at a time, out of...Ch. 8.4 - Create an interesting application whose solution...Ch. 8.4 - Create an interesting application whose solution...Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - In Exercises 1116, fill in the blanks using the...Ch. 8.5 - In Exercises 1116, fill in the blanks using the...Ch. 8.5 - In Exercises 1116, fill in the blanks using the...Ch. 8.5 - In Exercises 1116, fill in the blanks using the...Ch. 8.5 - In Exercises 1116, fill in the blanks using the...Ch. 8.5 - In Exercises 1116, fill in the blanks using the...Ch. 8.5 - In Exercises 1722, find the conditional...Ch. 8.5 - In Exercises 1722, find the conditional...Ch. 8.5 - In Exercises 1722, find the conditional...Ch. 8.5 - In Exercises 1722, find the conditional...Ch. 8.5 - In Exercises 1722, find the conditional...Ch. 8.5 - In Exercises 1722, find the conditional...Ch. 8.5 - Exercises 2328 require the use of counting...Ch. 8.5 - Exercises 2328 require the use of counting...Ch. 8.5 - Exercises 2328 require the use of counting...Ch. 8.5 - Exercises 2328 require the use of counting...Ch. 8.5 - Exercises 2328 require the use of counting...Ch. 8.5 - Exercises 2328 require the use of counting...Ch. 8.5 - In Exercises 2932, supply the missing quantities....Ch. 8.5 - In Exercises 2932, supply the missing quantities....Ch. 8.5 - In Exercises 2932, supply the missing quantities....Ch. 8.5 - In Exercises 2932, supply the missing quantities....Ch. 8.5 - In Exercises 3336, say whether the given pair of...Ch. 8.5 - In Exercises 3336, say whether the given pair of...Ch. 8.5 - In Exercises 3336, say whether the given pair of...Ch. 8.5 - In Exercises 3336, say whether the given pair of...Ch. 8.5 - In Exercises 3742, two dice (one red and one...Ch. 8.5 - In Exercises 3742, two dice (one red and one...Ch. 8.5 - In Exercises 3742, two dice (one red and one...Ch. 8.5 - In Exercises 3742, two dice (one red and one...Ch. 8.5 - In Exercises 3742, two dice (one red and one...Ch. 8.5 - In Exercises 3742, two dice (one red and one...Ch. 8.5 - If a coin is tossed 11 times, find the probability...Ch. 8.5 - If a die is rolled four times, find the...Ch. 8.5 - Personal Bankruptcy In 2004 the probability that a...Ch. 8.5 - Personal Bankruptcy In 2004 the probability that a...Ch. 8.5 - Existing Home Sales During the year ending April...Ch. 8.5 - Existing Home Sales Refer to the data given in...Ch. 8.5 - Social Security According to a New York Times/CBS...Ch. 8.5 - Social Security According to The New York...Ch. 8.5 - Marketing A market survey shows that 40% of the...Ch. 8.5 - Marketing A market survey shows that 60% of the...Ch. 8.5 - Road Safety In 1999 the probability that a...Ch. 8.5 - Road Safety In 1998 the probability that a...Ch. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Air Bag Safety According to a 2000 study conducted...Ch. 8.5 - Air Bag Safety According to the study cited in...Ch. 8.5 - Productivity A company wishes to enhance...Ch. 8.5 - Productivity Consider the events T and I in...Ch. 8.5 - Internet Use in 2000 The following pie chart shows...Ch. 8.5 - Internet Use in 2001 Repeat Exercise 83 using the...Ch. 8.5 - Auto Theft Exercises 8590 are based on the...Ch. 8.5 - Auto Theft Exercises 8590 are based on the...Ch. 8.5 - Auto Theft Exercises 8590 are based on the...Ch. 8.5 - Auto Theft Exercises 8590 are based on the...Ch. 8.5 - Auto Theft Exercises 8590 are based on the...Ch. 8.5 - Auto Theft Exercises 8590 are based on the...Ch. 8.5 - Drug Tests If 90% of the athletes who test...Ch. 8.5 - Fitness Tests If 80% of candidates for the soccer...Ch. 8.5 - Food Safety According to a University of Maryland...Ch. 8.5 - Food Safety According to the study mentioned in...Ch. 8.5 - Food Safety According to the study mentioned in...Ch. 8.5 - Food Safety According to the study mentioned in...Ch. 8.5 - Ultimate Hockey Cyber Video Games, Inc., the...Ch. 8.5 - Ultimate Hockey (See Exercise 97.) Cyber Video...Ch. 8.5 - The probability of misspelling Waner is p and is...Ch. 8.5 - The probability of spelling Waner correctly is p,...Ch. 8.5 - Name three events, each independent of the others,...Ch. 8.5 - Name three pairs of independent events when a pair...Ch. 8.5 - You wish to ascertain the probability of an event...Ch. 8.5 - Your television advertising campaign seems to have...Ch. 8.5 - You are having trouble persuading your friend...Ch. 8.5 - Your other friend Giuseppe is spreading rumors...Ch. 8.5 - If AB and P(B)0, why is P(A|B)=P(A)P(B)?Ch. 8.5 - If BA and P(B)0, why is P(A|B)=1?Ch. 8.5 - Your best friend thinks that it is impossible for...Ch. 8.5 - Another of your friends thinks that two mutually...Ch. 8.5 - Show that if A and B are independent, then so are...Ch. 8.5 - Show that if A and B are independent, then so are...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - Music Downloading According to a study on the...Ch. 8.6 - Music Downloading According to the study cited in...Ch. 8.6 - Weather It snows in Greenland an average of once...Ch. 8.6 - Weather It rains in Spain an average of once every...Ch. 8.6 - University Admissions In fall 2014, 34% of...Ch. 8.6 - University Admissions In fall 2014, 71% of...Ch. 8.6 - Side-Impact Hazard In 2004, 45.4% of all light...Ch. 8.6 - Side-Impact Hazard In 2004, 27.3% of all light...Ch. 8.6 - Athletic Fitness Tests Any athlete who fails the...Ch. 8.6 - Academic Testing Professor Frank Nabarro insists...Ch. 8.6 - Side-Impact Hazard (Compare Exercise 15.) In 2004,...Ch. 8.6 - Side-Impact Hazard In 1986, 23.9% of all light...Ch. 8.6 - University Admissions In fall 2008, UCLA admitted...Ch. 8.6 - University Admissions In fall 2002, UCLA admitted...Ch. 8.6 - Internet Use (Historical) In 2000, 86% of all...Ch. 8.6 - Internet Use (Historical) In 2000, 59% of all...Ch. 8.6 - Market Surveys A New York Times survey of...Ch. 8.6 - Crime and Preschool. A New York Times survey82 of...Ch. 8.6 - Grade Complaints Two of the mathematics professors...Ch. 8.6 - Weather Prediction A local TV station employs...Ch. 8.6 - Employment in the 1980s In a 1987 survey of...Ch. 8.6 - Employment in the 1980s Repeat Exercise 29 in the...Ch. 8.6 - Juvenile Delinquency According to a study at the...Ch. 8.6 - Crime According to the same study at the Oregon...Ch. 8.6 - Benefits of Exercise According to a study in The...Ch. 8.6 - Benefits of Exercise Repeat Exercise 33 assuming...Ch. 8.6 - Air Bag Safety According to a 2000 study conducted...Ch. 8.6 - Air BagSafety According to the study cited in...Ch. 8.6 - Your friend claims that the probability of A given...Ch. 8.6 - Complete the following sentence. To use Bayes...Ch. 8.6 - Give an example in which a steroids test gives a...Ch. 8.6 - Give an example in which a steroids test gives a...Ch. 8.6 - Use a tree to derive the expanded form of Bayes...Ch. 8.6 - Write down an expanded form of Bayes theorem that...Ch. 8.6 - Politics The following letter appeared in The New...Ch. 8.6 - Politics Refer back to Exercise 43. If the letter...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - Marketing A market survey shows that half the...Ch. 8.7 - Major Switching At Suburban Community College, 10%...Ch. 8.7 - Pest Control In an experiment to test the...Ch. 8.7 - Employment You have worked for the Department of...Ch. 8.7 - Risk Analysis An auto insurance company classifies...Ch. 8.7 - Debt Analysis A credit card company classifies its...Ch. 8.7 - Textbook Adoptions College instructors who adopt...Ch. 8.7 - Confidence Level Tommy the Dunkers performance on...Ch. 8.7 - Debt Analysis As the manager of a large retailing...Ch. 8.7 - Debt Analysis Repeat Exercise 45 using the...Ch. 8.7 - Market Share: Cell Phones Three of the largest...Ch. 8.7 - Dissipation Consider the following five-state...Ch. 8.7 - Dissipation with Drift Consider the following...Ch. 8.7 - Describe an interesting situation that can be...Ch. 8.7 - Describe an interesting situation that can be...Ch. 8.7 - Describe some drawbacks to using Markov processes...Ch. 8.7 - Can the repeated toss of a fair coin be modeled by...Ch. 8.7 - Explain: If Q is a matrix whose rows are...Ch. 8.7 - Construct a four-state Markov system so that both...Ch. 8.7 - Refer to the following state transition diagram,...Ch. 8.7 - Without doing any calculation, find the...Ch. 8.7 - Construct a regular state transition diagram that...Ch. 8.7 - Construct a regular state transition diagram that...Ch. 8.7 - Show that if a Markov system has two distinct...Ch. 8.7 - If higher and higher powers of P approach a fixed...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - A poll shows that half the consumers who use Brand...Ch. 8 - A poll shows that half the consumers who use Brand...Ch. 8 - A poll shows that half the consumers who use Brand...Ch. 8 - A poll shows that half the consumers who use Brand...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Sales According to statistics gathered by...Ch. 8 - Sales Repeat Exercise 51 in the event that 1% of...Ch. 8 - University Admissions In the year when Billy-Sean...Ch. 8 - University Admissions Billy-Sean OHagan had also...Ch. 8 - Competition As was mentioned earlier,...Ch. 8 - Competition As was mentioned earlier,...Ch. 8 - Competition As was mentioned earlier,...Ch. 8 - Competition As was mentioned earlier,...

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