a. To determine The probability values for P ( A ∩ B ) , P ( B ∩ C ) , P ( A ∪ C ) , P ( A ∪ B ∪ C ) , P ( B c ) , P ( A c ∩ B ) , P ( B | C ) and P ( B | A ) Explanation Given info: There is a Venn diagram showing the events A,B and C with sample points 1,2,3,4,5 and 6. The probability values of the sample points are, P ( 1 ) = 0.3 , P ( 2 ) = 0.2 , P ( 3 ) = 0.1 , P ( 4 ) = 0.1 , P ( 5 ) = 0.1 and P ( 6 ) = 0.2 Calculation: Event A ∩ B : There is no sample point in the event A ∩ B . Hence, the probability of the event A ∩ B is, P ( A ∩ B ) = 0 Event B ∩ C : The sample point in the event B ∩ C is 2. So, the probability of the event B ∩ C is, P ( B ∩ C ) = P ( 2 ) = 0.2 Event A ∪ C : The sample points in the event A ∪ C are 1, 2,3,5,6. So, the probability of the event A ∪ C is, P ( A ∪ C ) = P ( 1 ) + P ( 2 ) + P ( 3 ) + P ( 5 ) + P ( 6 ) Substitute, P ( 1 ) = 0.3 , P ( 2 ) = 0.2 , P ( 3 ) = 0.1 , P ( 5 ) = 0.1 and P ( 6 ) = 0.2 in the above equation. The required probability is obtained as shown below: P ( A ∪ C ) = P ( 1 ) + P ( 2 ) + P ( 3 ) + P ( 5 ) + P ( 6 ) = 0.3 + 0.2 + 0.1 + 0.1 + 0.2 = 0.9 The probability, P ( A ∪ C ) = 0.9 . Event A ∪ B ∪ C : The event A ∪ B ∪ C contains the sample points 1, 2,3,4,5 and 6. Thus, the probability of the event A ∪ B ∪ C is obtained as, P ( A ∪ B ∪ C ) = P ( 1 ) + P ( 2 ) + P ( 4 ) + P ( 5 ) + P ( 6 ) = 0.3 + 0.2 + 0.1 + 0.1 + 0.1 + 0.2 = 1 The probability, P ( A ∪ B ∪ C ) = 1 b. To determine To check: Whether the events A and B are mutually exclusive and independent and to explain the reason. c. To determine To check: Whether the events B and C are mutually exclusive and independent and to explain the reason.

13th Edition

ISBN: 9780134080215

Author: James T. McClave, Terry T Sincich

Publisher: PEARSON

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Chapter 3, Problem 154LM

To determine

The probability values for

P(A∩B),P(B∩C),P(A∪C),P(A∪B∪C),P(Bc),P(Ac∩B),P(B|C) and P(B|A)

To determine

To check: Whether the events A and B are mutually exclusive and independent and to explain the reason.

To determine

To check: Whether the events B and C are mutually exclusive and independent and to explain the reason.

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Chapter 3, Problem 153LM

Chapter 3, Problem 155LM

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Chapter 3 Solutions

Statistics (13th Edition)

Ch. 3.1 - What is an experiment? Ch. 3.1 - What are the most basic outcomes of an experiment...Ch. 3.1 - Define the sample space. Ch. 3.1 - What is a Venn diagram? Ch. 3.1 - Give two probability rules for sample points. Ch. 3.1 - What is an event? Ch. 3.1 - How do you find the probability of an event made...Ch. 3.1 - Give a scenario where the combinations rule is...Ch. 3.1 - 3.1 An experiment results in one of the following...Ch. 3.1 - The following Venn diagram describes the sample...

Ch. 3.1 - 3.3 The sample space for an experiment contains...Ch. 3.1 - 3.4 Compute each of the following: Ch. 3.1 - 3.5 Compute the number of ways you can select n...Ch. 3.1 - Two fair dice are tossed, and the up face on each...Ch. 3.1 - 3.7 Two marbles are drawn at random and without...Ch. 3.1 - Simulate the experiment described in Exercise...Ch. 3.1 - Use the applet Simulating the Probability of...Ch. 3.1 - Use the applet Simulating the Probability of a...Ch. 3.1 - Do social robots walk or roll? Refer to the...Ch. 3.1 - Crop damage by wild boars. The level of crop...Ch. 3.1 - 3.11 Colors of M&M’s candies. When they were first...Ch. 3.1 - Rare underwater sounds. A study of underwater...Ch. 3.1 - USDA chicken inspection. The United States...Ch. 3.1 - African rhinos. Two species of rhinoceros native...Ch. 3.1 - STEM experiences for girls. Refer to the 2013...Ch. 3.1 - Health risks to beachgoers. According to a...Ch. 3.1 - Cheek teeth of extinct primates. Refer to the...Ch. 3.1 - Chance of rain. Answer the following question...Ch. 3.1 - Prob. 27ACI Ch. 3.1 - Museum management. Refer to the Museum Management...Ch. 3.1 - 3.109 Choosing portable grill displays. Consider a...Ch. 3.1 - Prob. 30ACI Ch. 3.1 - 3.22 Jai-alai bets. The Quinella bet at the...Ch. 3.1 - Using game simulation to teach a course. In...Ch. 3.1 - Lead bullets as forensic evidence. Chance (Summer...Ch. 3.1 - Matching socks. Consider the following question...Ch. 3.1 - Post-op nausea study. Nausea and vomiting after...Ch. 3.1 - Dominant versus recessive traits. An individual’s...Ch. 3.1 - Drug testing of firefighters. Hillsborough County,...Ch. 3.4 - Define in words mutually exclusive events. Ch. 3.4 - Define in words the union of two events. Ch. 3.4 - Define in words the intersection of two events. Ch. 3.4 - Define in words the complement of an event. Ch. 3.4 - Prob. 42UP Ch. 3.4 - State the additive rule of probability for...Ch. 3.4 - State the additive rule of probability for any two...Ch. 3.4 - 3.31 A fair coin is tossed three times, and the...Ch. 3.4 - 3.30 Suppose P (A) = A, P(B) = 7, and P (A ∩ B) =...Ch. 3.4 - 3.33 Consider the Venn diagram below, where P(E1)...Ch. 3.4 - Consider the following Venn diagram, where P(E1) =...Ch. 3.4 - 3.32 A pair of fair dice is tossed. Define the...Ch. 3.4 - Three fair coins are tossed. We wish to find the...Ch. 3.4 - The outcomes of two variables are (Low. Medium....Ch. 3.4 - Use the applets Simulating the Probability of...Ch. 3.4 - Use the applets Simulating the Probability of...Ch. 3.4 - Social networking. According to the Pew Research...Ch. 3.4 - 3.37 Do social robots walk or roll? Refer to the...Ch. 3.4 - 3.39 Study of analysts' forecasts. The Journal of...Ch. 3.4 - Gene expression profiling. Gene expression...Ch. 3.4 - 3.41 Scanning errors at Walmart. The National...Ch. 3.4 - Sleep apnea and sleep stage transitioning. Sleep...Ch. 3.4 - Attempted suicide methods. A study of attempted...Ch. 3.4 - 3.48 Guilt in decision making. The effect of guilt...Ch. 3.4 - Prob. 60ACI Ch. 3.4 - Fighting probability of fallow deer bucks. In...Ch. 3.4 - 3.47 Cell phone handoff behavior. A "handoff' is a...Ch. 3.4 - Chemical signals of mice. The ability of a mouse...Ch. 3.4 - Employee behavior problems. The Organizational...Ch. 3.4 - Cloning credit or debit cards. Wireless identity...Ch. 3.4 - 3.50 Galileo's Passedix game. Passedix is a game...Ch. 3.4 - 3.51 Encoding variability in software. At the 2012...Ch. 3.6 - Explain the difference between an unconditional...Ch. 3.6 - Give the multiplicative rule of probability...Ch. 3.6 - Give the formula for finding P(B|A). Ch. 3.6 - Defend or refute each of the following...Ch. 3.6 - 3.52 For two events, A and B, P (A) − .4, P (B) −...Ch. 3.6 - 3.53 For two events, A and B, P (A) = .4, P (B) =...Ch. 3.6 - An experiment results in one of three mutually...Ch. 3.6 - 3.55 For two independent events, A and B, P (A) =...Ch. 3.6 - An experiment results in one of five sample points...Ch. 3.6 - Consider the experiment defined by the...Ch. 3.6 - 3.59 A sample space contains six sample points and...Ch. 3.6 - 3.58 Two fair dice are tossed, and the following...Ch. 3.6 - A box contains two white, two red, and two blue...Ch. 3.6 - Use the applet Simulating the Probability of...Ch. 3.6 - 3.63 Blood diamonds. According to Global Research...Ch. 3.6 - 3.64 Do social robots walk or roll? Refer to the...Ch. 3.6 - Crop damage by wild boars. Refer to the Current...Ch. 3.6 - Cardiac stress testing. In addition to standard...Ch. 3.6 - National firearms survey. The Harvard School of...Ch. 3.6 - Guilt in decision making. Refer to the Journal of...Ch. 3.6 - Speeding linked to fatal car crashes. According to...Ch. 3.6 - Appraisals and negative emotions. According to...Ch. 3.6 - Prob. 89ACI Ch. 3.6 - Sleep apnea and sleep stage transitioning. Refer...Ch. 3.6 - 3.73 Firefighters' use of gas detection devices....Ch. 3.6 - Compensatory advantage in education. According to...Ch. 3.6 - 3.75 Are you really being served red snapper? Red...Ch. 3.6 - Fighting probability of fallow deer bucks. Refer...Ch. 3.6 - Extinct New Zealand birds. Refer to the...Ch. 3.6 - Muscle, fat, and bone issues while aging. In...Ch. 3.6 - 3.71 Ambulance response time. Geographical...Ch. 3.6 - Intrusion detection systems. A computer intrusion...Ch. 3.6 - Detecting traces of TNT. University of Florida...Ch. 3.6 - Random mutation of cells. Chance (Spring 2010)...Ch. 3.6 - Testing a psychic’s ability. Consider an...Ch. 3.6 - 3.78 Risk of a natural gas pipeline accident....Ch. 3.6 - 3.80 Encryption systems with erroneous...Ch. 3.7 - Give a scenario where the multiplicative rule...Ch. 3.7 - Give a scenario where the permutations rule...Ch. 3.7 - Give a scenario where the partitions rule...Ch. 3.7 - What is the difference between the permutations...Ch. 3.7 - Find the numerical values of Ch. 3.7 - Use the multiplicative rule to determine the...Ch. 3.7 - Determine the number of sample points contained in...Ch. 3.7 - An experiment consists of choosing objects without...Ch. 3.7 - Cheek teeth of extinct primates. Refer to the...Ch. 3.7 - Choosing portable grill displays. Refer to the...Ch. 3.7 - Monitoring impedance to leg movements. In an...Ch. 3.7 - Picking a basketball team. Suppose you are to...Ch. 3.7 - Selecting project teams. Suppose you are managing...Ch. 3.7 - 3.125 Using game simulation to teach a course. In...Ch. 3.7 - U.S. ZIP codes. The nine-digit ZIP code has become...Ch. 3.7 - Traveling between cities. A salesperson living in...Ch. 3.7 - Football uniform combinations. Nike manufactures...Ch. 3.7 - Kiwifruit as an iron supplement. An article...Ch. 3.7 - Randomization in a study of TV commercials....Ch. 3.7 - Multilevel marketing schemes. Successful companies...Ch. 3.7 - Mathematical theory of partitions. Mathematicians...Ch. 3.7 - The “marriage” problem. A mathematics assignment...Ch. 3.7 - Florida license plates. In the mid-1980s, the...Ch. 3.7 - Selecting a maintenance support system. In the...Ch. 3.7 - Volleyball positions. Intercollegiate volleyball...Ch. 3.7 - Studying exam questions. A college professor hands...Ch. 3.7 - Modeling the behavior of granular media. Granular...Ch. 3.7 - A straight flush in poker. Consider 5-card poker...Ch. 3.8 - Explain the difference between the two...Ch. 3.8 - Why is Bayes’s rule unnecessary for finding P(B|A)...Ch. 3.8 - Why is Bayes’s rule unnecessary for finding P(B|A)...Ch. 3.8 - 3.81 Suppose the events B1 and B2 are mutually...Ch. 3.8 - 3.82 Suppose the events B1, B2, and B3 are...Ch. 3.8 - 3.83 Suppose the events B1, B2, and B3 are...Ch. 3.8 - Reverse-engineering gene identification. In...Ch. 3.8 - 3.122 Drug testing in athletes. When Olympic...Ch. 3.8 - 3.85 Fingerprint expertise. A study published in...Ch. 3.8 - 3.86 Tests for Down syndrome. Currently, there are...Ch. 3.8 - HIV testing and false positives. Bayes’s rule was...Ch. 3.8 - 3.89 Mining for dolomite. Dolomite is a valuable...Ch. 3.8 - 3.90 Nondestructive evaluation. Nondestructive...Ch. 3.8 - 3.92 Intrusion detection systems. The Journal of...Ch. 3.8 - Confidence of feedback information for improving...Ch. 3.8 - 3.93 Forensic analysis of JFK assassination...Ch. 3 - Prob. 148UP Ch. 3 - Use the symbols ⋂, ⋃, |, and c to convert the...Ch. 3 - 3.95 A sample space consists of four sample...Ch. 3 - 3.97 A and B are mutually exclusive events, with P...Ch. 3 - 3.96 For two events A and B, suppose P (A) = .7, P...Ch. 3 - 3.99 Given that P (A∩B) = .4 and P (A|B) = .8,...Ch. 3 - 3.101 The Venn diagram below illustrates a sample...Ch. 3 - A fair die is tossed, and the up face is noted. If...Ch. 3 - A balanced die is thrown once. If a 4 appears, a...Ch. 3 - Two events, A and B, are independent, with P(A) =...Ch. 3 - Find the numerical value of 6! 0! Ch. 3 - Use the applet entitled Random Numbers to generate...Ch. 3 - Going online for health information. A...Ch. 3 - Study of ancient pottery. Refer to the Chance...Ch. 3 - Post office violence. The Wall Street Journal...Ch. 3 - Sterile couples in Jordan. A sterile family is a...Ch. 3 - 3.107 New car crash tests. Refer to the National...Ch. 3 - Selecting a sample. A random sample of five...Ch. 3 - Fungi in beech forest trees. The current status of...Ch. 3 - Do you have a library card? According to a Harris...Ch. 3 - Beach erosional hot spots. Beaches that exhibit...Ch. 3 - Chemical insect attractant. An entomologist is...Ch. 3 - Toxic chemical incidents. Process Safety Progress...Ch. 3 - Prob. 170ACI Ch. 3 - Winning at roulette. Roulette is a very popular...Ch. 3 - Cigar smoking and cancer. The Journal of the...Ch. 3 - Errors in estimating job costs. A construction...Ch. 3 - Elderly wheelchair user study. The American...Ch. 3 - Prob. 175ACI Ch. 3 - Prob. 176ACI Ch. 3 - Shooting free throws. In college basketball games,...Ch. 3 - Prob. 178ACI Ch. 3 - Prob. 179ACI Ch. 3 - Prob. 180ACI Ch. 3 - Prob. 181ACI Ch. 3 - 3.112 Monitoring quality of power equipment....Ch. 3 - Prob. 183ACI Ch. 3 - Dream experiment in psychology. A clinical...Ch. 3 - Prob. 185ACI Ch. 3 - Forest fragmentation study. Refer to the...Ch. 3 - Odds of winning a horse race. Handicappers for...Ch. 3 - Sex composition patterns of children in families....Ch. 3 - Finding an organ transplant match. One of the...Ch. 3 - 3.131 Chance of winning blackjack. Blackjack, a...Ch. 3 - Accuracy of pregnancy tests. Seventy-five percent...Ch. 3 - 3.130 Chance of winning at “craps.” A version of...Ch. 3 - The perfect bridge hand. According to a morning...Ch. 3 - Odd Man Out. Three people play a game called “Odd...Ch. 3 - 3.133 “Let’s Make a Deal.” Marilyn vos Savant, who...Ch. 3 - Most likely coin-toss sequence. In Parade...

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The probability values for P ( A ∩ B ) , P ( B ∩ C ) , P ( A ∪ C ) , P ( A ∪ B ∪ C ) , P ( B c ) , P ( A c ∩ B ) , P ( B | C ) and P ( B | A )

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The probability values for P(A∩B),P(B∩C),P(A∪C),P(A∪B∪C),P(Bc),P(Ac∩B),P(B|C) and P(B|A)

To check: Whether the events A and B are mutually exclusive and independent and to explain the reason.

To check: Whether the events B and C are mutually exclusive and independent and to explain the reason.

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Chapter 3 Solutions

The probability values for

P(A∩B),P(B∩C),P(A∪C),P(A∪B∪C),P(Bc),P(Ac∩B),P(B|C) and P(B|A)