Answer: In Exercise, use the drug screening data given in

Complements What is wrong with the expression \(P(A)+P\left(A^{-}\right)=0.5\) ? Equation Transcription: Text Transcription: P(A) + P(A-)=0.5

Problem 3BSC Disjoint Events For a Gallup poll, M is the event of randomly selecting a male, and R is the event of randomly selecting a Republican. Are events M and R disjoint? Why or why not?

Casino Craps A gambler plans to play the casino dice game called craps, and he plans to place a bet on the “pass line.” Let A be the event of winning. Based on the rules used in almost all casinos, \(P(A)=244 / 495\) . Describe the event \(A^{-}\) and find the value of \(P\left(A^{-}\right)\) . Equation Transcription: Text Transcription: P (A)=244 / 495 A- P(A-)

Rule of Complements One form of the rule of complements is this: \(P\left(A \text { or } A^{-}\right)=1\). Write a sentence describing the message that this rule represents. Equation Transcription: Text Transcription: P (A or A- )=1

Problem 5BSC Determining Whether Events Are Disjoint. For Exercise, determine whether the two events are disjoint for a single trial. (Hint: Consider “disjoint” to be equivalent to “separate” or “not overlapping.”) Arriving late for your next statistics class. Arriving early for your next statistics class.

Problem 6BSC Determining Whether Events Are Disjoint. For Exercise, determine whether the two events are disjoint for a single trial. (Hint: Consider “disjoint” to be equivalent to “separate” or “not overlapping.”) Asking for a date through a Twitter post. Asking for a date in French, the romance language.

Problem 7BSC Determining Whether Events Are Disjoint. For Exercise, determine whether the two events are disjoint for a single trial. (Hint: Consider “disjoint” to be equivalent to “separate” or “not overlapping.”) Randomly selecting a survey respondent and getting someone who believes in UFOs. Randomly selecting a survey respondent and getting someone who believes in the devil.

Problem 9BSC Determining Whether Events Are Disjoint. For Exercise, determine whether the two events are disjoint for a single trial. (Hint: Consider “disjoint” to be equivalent to “separate” or “not overlapping.”) Randomly selecting a drug screening result and getting one that is a false negative. Randomly selecting a drug screening result and getting one from someone who is not a drug user.

Problem 10BSC Determining Whether Events Are Disjoint. For Exercise, determine whether the two events are disjoint for a single trial. (Hint: Consider “disjoint” to be equivalent to “separate” or “not overlapping.”) Randomly selecting a drug screening result and getting one that is a false positive. Randomly selecting a drug screening result and getting one from someone who uses drugs.

Problem 8BSC Determining Whether Events Are Disjoint. For Exercise, determine whether the two events are disjoint for a single trial. (Hint: Consider “disjoint” to be equivalent to “separate” or “not overlapping.”) Randomly selecting a statistics student and getting one who uses a TI calculator in class. Randomly selecting a statistics student and getting one who uses the STATDISK computer program.

Problem 11BSC Determining Whether Events Are Disjoint. For Exercise, determine whether the two events are disjoint for a single trial. (Hint: Consider “disjoint” to be equivalent to “separate” or “not overlapping.”) Randomly selecting a drug screening result and getting one that is a false positive. Randomly selecting a drug screening result and getting one from someone who does not use drugs.

Problem 12BSC Determining Whether Events Are Disjoint. For Exercise, determine whether the two events are disjoint for a single trial. (Hint: Consider “disjoint” to be equivalent to “separate” or “not overlapping.”) Randomly selecting a drug screening result and getting one that is a false positive. Randomly selecting a drug screening result and getting one that is a false negative.

Problem 13BSC Finding Complements. In Exercise, find the indicated complements. Whatever A Marist poll survey showed that 47% of respondents chose “whatever” as the most annoying phrase used in conversation. What is the probability of randomly selecting someone choosing something different from “whatever” as the most annoying phrase in conversation?

Problem 14BSC Finding Complements. In Exercise, find the indicated complements. Online Courses According to the National Association for College Admissions Counseling and USA Today, 19.8% of college students take at least one class online. What is the probability of randomly selecting a college student who does not take any college courses online?

Problem 15BSC Finding Complements. In Exercise, find the indicated complements. Flirting Survey In a Microsoft Instant Messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D) = 0.550, where D is directly in person. If someone is randomly selected, what does P(D) represent, and what is its value?

Problem 16BSC Finding Complements. In Exercise, find the indicated complements. Sobriety Checkpoint When the author observed a sobriety checkpoint conducted by the Dutchess County Sheriff department, he saw that 676 drivers were screened and 6 were arrested for driving while intoxicated. Based on those results, we can estimate that P(I) = 0.00888, where Idenotes the event of screening a driver and getting someone who is intoxicated. What does P(I) denote, and what is its value?

In Exercises 17–20, use the drug screening data given in Table 41, which is included with the Chapter Problem. Drug Screening If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or a negative test result.

In Exercises 17–20, use the drug screening data given in Table 41, which is included with the Chapter Problem. Drug Screening If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or does not use drugs.

In Exercises 17–20, use the drug screening data given in Table 41, which is included with the Chapter Problem. Drug Screening If one of the subjects is randomly selected, find the probability that the subject had a negative test result or does not use drugs.

In Exercises 17–20, use the drug screening data given in Table 41, which is included with the Chapter Problem. Drug Screening If one of the subjects is randomly selected, find the probability that the subject had a negative test result or uses drugs.

Problem 21BSC Dosage Calculations. ?In Exercise?, ?use the data in the accompanying table, which lists the numbers of correct and wrong dosage amounts calculated by physicians. In a research experiment, one group of physicians was given bottles of epinephrine labeled with a?concentration ?of “1 milligram in 1milliliter solution,” and another group of physicians was given bottles labeled with a ratio ?of “1milliliterof a 1:1000 solution.” The two labels describe the exact same amount, and the physicians were instructed to administer 0.12 milligrams of epinephrine. The results were reported in? ew York Times. Cor Wr rect ong Dos Dos age age Cal Cal cula cula tion tion Concen tration Label 11 3 (“1 milligra m in 1 millilite r solution ”) Ratio Label (“1 millilite 2 12 r of a 1:1000 solution ”) Correct Dosage If one of the physicians is randomly selected, what is the probability of getting one who calculated the dose correctly? Is that probability as high as it should be?

Problem 22BSC Dosage Calculations. In Exercise, use the data in the accompanying table, which lists the numbers of correct and wrong dosage amounts calculated by physicians. In a research experiment, one group of physicians was given bottles of epinephrine labeled with aconcentration of “1 milligram in 1milliliter solution,” and another group of physicians was given bottles labeled with a ratio of “1milliliterof a 1:1000 solution.” The two labels describe the exact same amount, and the physicians were instructed to administer 0.12 milligrams of epinephrine. The results were reported in the New York Times. Correct Dosage Calculation Wrong Dosage Calculation Concentration Label (“1 milligram in 1 milliliter solution”) 11 3 Ratio Label (“1 milliliter of a 1:1000 solution”) 2 12 Wrong Dosage If one of the physicians is randomly selected, what is the probability of getting one who calculated the dose incorrectly? Is that probability as low as it should be?

Problem 23BSC Dosage Calculations. In Exercise, use the data in the accompanying table, which lists the numbers of correct and wrong dosage amounts calculated by physicians. In a research experiment, one group of physicians was given bottles of epinephrine labeled with aconcentration of “1 milligram in 1milliliter solution,” and another group of physicians was given bottles labeled with a ratio of “1milliliterof a 1:1000 solution.” The two labels describe the exact same amount, and the physicians were instructed to administer 0.12 milligrams of epinephrine. The results were reported in the New York Times. Correct Dosage Calculation Wrong Dosage Calculation Concentration Label (“1 milligram in 1 milliliter solution”) 11 3 Ratio Label (“1 milliliter of a 1:1000 solution”) 2 12 Correct or Concentration If one of the physicians is randomly selected, find the probability of getting one who made a correct dosage calculation or was given the bottle with a concentration label.

Problem 24BSC Dosage Calculations. In Exercise, use the data in the accompanying table, which lists the numbers of correct and wrong dosage amounts calculated by physicians. In a research experiment, one group of physicians was given bottles of epinephrine labeled with aconcentration of “1 milligram in 1milliliter solution,” and another group of physicians was given bottles labeled with a ratio of “1milliliterof a 1:1000 solution.” The two labels describe the exact same amount, and the physicians were instructed to administer 0.12 milligrams of epinephrine. The results were reported in the New York Times. Correct Dosage Calculation Wrong Dosage Calculation Concentration Label (“1 milligram in 1 milliliter solution”) 11 3 Ratio Label (“1 milliliter of a 1:1000 solution”) 2 12 Wrong Dosage or Ratio If one of the physicians is randomly selected, find the probability of getting one who made a wrong dosage calculation or was given the bottle with a ratio label.

Problem 25BSC Dosage Calculations. In Exercise, use the data in the accompanying table, which lists the numbers of correct and wrong dosage amounts calculated by physicians. In a research experiment, one group of physicians was given bottles of epinephrine labeled with aconcentration of “1 milligram in 1milliliter solution,” and another group of physicians was given bottles labeled with a ratio of “1milliliterof a 1:1000 solution.” The two labels describe the exact same amount, and the physicians were instructed to administer 0.12 milligrams of epinephrine. The results were reported in the New York Times. Correct Dosage Calculation Wrong Dosage Calculation Concentration Label (“1 milligram in 1 milliliter solution”) 11 3 Ratio Label (“1 milliliter of a 1:1000 solution”) 2 12 Which Group Did Better? a. For the physicians given the bottles labeled with a concentration, find the percentage of correct dosage calculations, then express it as a probability. ________________ b. For the physicians given the bottles labeled with a ratio, find the percentage of correct dosage calculations; then express it as a probability. ________________ c. Does it appear that either group did better? What does the result suggest about drug labels?

Problem 26BSC Dosage Calculations. In Exercise, use the data in the accompanying table, which lists the numbers of correct and wrong dosage amounts calculated by physicians. In a research experiment, one group of physicians was given bottles of epinephrine labeled with aconcentration of “1 milligram in 1milliliter solution,” and another group of physicians was given bottles labeled with a ratio of “1milliliterof a 1:1000 solution.” The two labels describe the exact same amount, and the physicians were instructed to administer 0.12 milligrams of epinephrine. The results were reported in the New York Times. Correct Dosage Calculation Wrong Dosage Calculation Concentration Label (“1 milligram in 1 milliliter solution”) 11 3 Ratio Label (“1 milliliter of a 1:1000 solution”) 2 12 Which Group Did Worse? a. For the physicians given the bottles labeled with a concentration, find the percentage of wrong dosage calculations; then express it as a probability. ________________ b. For the physicians given the bottles labeled with a ratio, find the percentage of wrong dosage calculations; then express it as a probability. ________________ c. Does it appear that either group did worse? What does the result suggest about drug labels?

Problem 27BSC Survey Refusals. In Exercise, refer to the following table summarizing results from a study of people who refused to answer survey questions (based on data from “I Hear You Knocking but You Can’t Come In,” by Fitzgerald and Fuller, Sociological Methods and Research, Vol. 11, No. 1). In each case, assume that one of the subjects is randomly selected. Age 18–21 22–29 30–39 40–49 50–59 60 and over Responded 73 255 245 136 138 202 Refused 11 20 33 16 27 49 Survey Refusals What is the probability that the selected person refused to answer? Does that probability value suggest that refusals are a problem for pollsters? Why or why not?

Problem 28BSC Survey Refusals. In Exercise, refer to the following table summarizing results from a study of people who refused to answer survey questions (based on data from“I Hear You Knocking but You Can’t Come In,” by Fitzgerald and Fuller, Sociological Methods and Research, Vol. 11, No. 1). In each case, assume that one of the subjects is randomly selected. Age 18–21 22–29 30–39 40–49 50–59 60 and over Responded 73 255 245 136 138 202 Refused 11 20 33 16 27 49 Survey Refusals A pharmaceutical company is interested in opinions of the elderly, because they are either receiving Medicare or will receive it soon. What is the probability that the selected subject is someone 60 and over who responded?

Problem 29BSC Survey Refusals. In Exercise, refer to the following table summarizing results from a study of people who refused to answer survey questions (based on data from“I Hear You Knocking but You Can’t Come In,” by Fitzgerald and Fuller, Sociological Methods and Research, Vol. 11, No. 1). In each case, assume that one of the subjects is randomly selected. Age 18–21 22–29 30–39 40–49 50–59 60 and over Responded 73 255 245 136 138 202 Refused 11 20 33 16 27 49 Survey Refusals What is the probability that the selected person responded or is in the 18–21 age bracket?

Problem 30BSC Survey Refusals. In Exercise, refer to the following table summarizing results from a study of people who refused to answer survey questions (based on data from“I Hear You Knocking but You Can’t Come In,” by Fitzgerald and Fuller, Sociological Methods and Research, Vol. 11, No. 1). In each case, assume that one of the subjects is randomly selected. Age 18–21 22–29 30–39 40–49 50–59 60 and over Responded 73 255 245 136 138 202 Refused 11 20 33 16 27 49 Survey Refusals What is the probability that the selected person refused to respond or is over 59 years of age?

Problem 31BSC Survey Refusals. In Exercise, refer to the following table summarizing results from a study of people who refused to answer survey questions (based on data from“I Hear You Knocking but You Can’t Come In,” by Fitzgerald and Fuller, Sociological Methods and Research, Vol. 11, No. 1). In each case, assume that one of the subjects is randomly selected. Age 18–21 22–29 30–39 40–49 50–59 60 and over Responded 73 255 245 136 138 202 Refused 11 20 33 16 27 49 Survey Refusals A market researcher is interested in responses, especially from those between the ages of 22 and 39, because they are the people more likely to make purchases. Find the probability that a selected subject responds or is between the ages of 22 and 39.

Problem 32BSC Survey Refusals. In Exercise, refer to the following table summarizing results from a study of people who refused to answer survey questions (based on data from“I Hear You Knocking but You Can’t Come In,” by Fitzgerald and Fuller, Sociological Methods and Research, Vol. 11, No. 1). In each case, assume that one of the subjects is randomly selected. Age 18–21 22–29 30–39 40–49 50–59 60 and over Responded 73 255 245 136 138 202 Refused 11 20 33 16 27 49 Survey Refusals A market researcher is not interested in refusals or subjects below 22 years of age or over 59. Find the probability that the selected person refused to answer or is below 22 or is older than 59.

In Exercises 33–38, use these results from the “1PanelTHC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results? among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.) Screening for Marijuana Use a. How many subjects are included in the study? b. How many subjects did not use marijuana? c. What is the probability that a randomly selected subject did not use marijuana?

In Exercises 33–38, use these results from the “1PanelTHC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results? among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.) Screening for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject tested positive or used marijuana.

In Exercises 33–38, use these results from the “1PanelTHC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results? among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.) Screening for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana.

In Exercises 33–38, use these results from the “1PanelTHC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results? among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.) Screening for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject actually used marijuana. Do you think that the result reflects the marijuana use rate in the general population?

In Exercises 33–38, use these results from the “1PanelTHC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results? among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.) Screening for Marijuana Use Find the probability of a false positive or false negative. What does the result suggest about the test's accuracy?

Problem 40BB Disjoint Events If events A and B are disjoint and events B and C are disjoint, must events A and C be disjoint? Give an example supporting your answer.

Exclusive Or The formal addition rule expressed the probability of A or B as follows: \(P(A \text { or } B)=P(A)+(B)-P(A \text { and } B)\). The exclusive or means either one or the other events occurs, but not both. Rewrite the expression for \(P(A \text { or } B)\) assuming that the addition rule uses the exclusive or instead of the inclusive or. (Hint: Draw a Venn diagram.) Equation Transcription: Text Transcription: P (A or B)=P( A)+( B)-P (A and B) P (A or B)

In Exercises 33–38, use these results from the “1PanelTHC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results? among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 41, which is included with the Chapter Problem.) Screening for Marijuana Use Find the probability of a correct result by finding the probability of a true positive or a true negative. How does this result relate to the result from Exercise 37?

Problem 42BB Extending the Addition Rule Extend the formal addition rule to develop an expression for P(A or B or C ). (Hint: Draw a Venn diagram.)

Problem 39BB Gender Selection When analyzing results from a test of the MicroSort gender-selection technique developed by the Genetics&IVF Institute, a researcher wants to compare the results to those obtained from a coin toss. Assume that boys and girls are equally likely and find P(G or H ), which is the probability of getting a baby girl or getting heads from a coin toss.

Complements and the Addition Rule a. Develop a formula for the probability of not getting either A or B on a single trial. That is, find an expression for \(P\left(A \text { or } B^{-}\right)\) b. Develop a formula for the probability of not getting A or not getting B on a single trial. That is, find an expression for \(P\left(A \text { or } B^{-}\right)\) c. Compare the results from parts (a) and (b). Does \(P\left(A \text { or } B^{-}\right)=P\left(A^{-} \text {or } B^{-}\right)\)? Equation Transcription: Text Transcription: P ( A or B-) P ( A or B-) P ( A or B-)=P (A- or B-)