Deck 4: B: probability and Probability Distributions

Question 1

Political Opinions Narrative
A political scientist asked a group of people how they felt about two political policy statements. Each person was to respond either A (agree), N (neutral), or D (disagree) to each policy statement.
Refer to Political Opinions Narrative. Assuming each response combination in the sample space is equally likely, what is the probability the person being interviewed agrees with at least one of the two policy statements?

Answer 1

5/9 0.556

Question 2

Job Applicants Narrative
Five applicants apply for two jobs. Applicants A and B are male; applicants C, D, and E are female. The personnel officer selects two applicants at random to fill the two jobs.
Refer to Job Applicants Narrative. If the two jobs are different, and denotes the collection of outcomes where the successful job applicants include exactly one female, what is P( )?
NAR: Job Applicants Narrative

Answer 2

P( ) = 12/20 = 0.6

Question 3

Political Opinions Narrative
A political scientist asked a group of people how they felt about two political policy statements. Each person was to respond either A (agree), N (neutral), or D (disagree) to each policy statement.
Refer to Political Opinions Narrative. Assuming each response combination in the sample space is equally likely, what is the probability the person being interviewed agrees with exactly one of the two political policy statements?

Answer 3

4/9 0.444

Question 4

Job Applicants Narrative
Five applicants apply for two jobs. Applicants A and B are male; applicants C, D, and E are female. The personnel officer selects two applicants at random to fill the two jobs.
Refer to Job Applicants Narrative. If the two jobs are different, and denotes the collection of outcomes where the successful job applicants include at least one female, what is P( )?

Question 5

Coffee Brands Narrative
A food company plans to conduct an experiment to compare its brand of coffee with that of two competitors. A single person is hired to taste each of three brands of coffee, which are unmarked except for identifying symbols, A, B, and C.
Refer to Coffee Brands Narrative. Define the experiment.

Question 6

Job Applicants Narrative
Five applicants apply for two jobs. Applicants A and B are male; applicants C, D, and E are female. The personnel officer selects two applicants at random to fill the two jobs.
Refer to Job Applicants Narrative. If the two jobs are different, and denotes the collection of outcomes where the successful job applicants include at least one male, what is P( )?

Question 7

Driver Education Narrative
Three randomly chosen 14-year-old middle school students who had not yet taken driver's education classes were given the written part of the Manitoba Driver's Exam. Each student was graded as passing (P) or failing (F) the written exam.
Refer to Driver Education Narrative. Assume each combination in the sample space is equally likely. Then, if you knew that at least one student passed the test, what is the probability all three students passed the test?

Question 8

Political Opinions Narrative
A political scientist asked a group of people how they felt about two political policy statements. Each person was to respond either A (agree), N (neutral), or D (disagree) to each policy statement.
Refer to Political Opinions Narrative. Describe the sample space; that is, list all possible response combinations to the two statements.

Question 9

Driver Education Narrative
Three randomly chosen 14-year-old middle school students who had not yet taken driver's education classes were given the written part of the Manitoba Driver's Exam. Each student was graded as passing (P) or failing (F) the written exam.
Maria selected two M&M candies at random from a bowl containing three M&Ms. One was red; one was yellow; and the remaining one was orange. Describe the sample space if the sampling is done with replacement.

Question 10

SALES NARRATIVE
A salesperson either makes a sale (S) or does not make a sale (N) with each of two potential customers. The simple events and their probabilities are given below.
Refer to Sales Narrative. What is the probability that exactly one sale is made?

Question 11

Job Applicants Narrative
Five applicants apply for two jobs. Applicants A and B are male; applicants C, D, and E are female. The personnel officer selects two applicants at random to fill the two jobs.
Refer to Job Applicants Narrative. List all possible combinations of the five applicants for the two different jobs.

Question 12

Job Applicants Narrative
Five applicants apply for two jobs. Applicants A and B are male; applicants C, D, and E are female. The personnel officer selects two applicants at random to fill the two jobs.
A sample space S consists of five simple events with the following probabilities:
P( ) = P( ) = 0.20, P( ) = 0.45, and P( ) = 2P( ).
a. Find the probabilities for simple events and .
b. Find the probabilities for these two events: A: , , and B: , .
c. List the simple events that are in either event A or event B or both.
d. List the simple events that are in both event A and event B.

Question 13

SALES NARRATIVE
A salesperson either makes a sale (S) or does not make a sale (N) with each of two potential customers. The simple events and their probabilities are given below.
Refer to Sales Narrative. What is the probability that exactly two sales were made?

Question 14

Job Applicants Narrative
Five applicants apply for two jobs. Applicants A and B are male; applicants C, D, and E are female. The personnel officer selects two applicants at random to fill the two jobs.
Refer to Job Applicants Narrative. If the two jobs are different, and denotes the collection of outcomes where the successful job applicants include exactly one male, what is P( )?

Question 15

Driver Education Narrative
Three randomly chosen 14-year-old middle school students who had not yet taken driver's education classes were given the written part of the Manitoba Driver's Exam. Each student was graded as passing (P) or failing (F) the written exam.
Refer to Driver Education Narrative. Describe the sample space; that is, list all possible combinations of the three students' grades.

Question 16

Political Opinions Narrative
A political scientist asked a group of people how they felt about two political policy statements. Each person was to respond either A (agree), N (neutral), or D (disagree) to each policy statement.
Refer to Political Opinions Narrative. Assuming each response combination in the sample space is equally likely, what is the probability the person being interviewed agrees with both of the two political policy statements?

Question 17

SALES NARRATIVE
A salesperson either makes a sale (S) or does not make a sale (N) with each of two potential customers. The simple events and their probabilities are given below.
Refer to Sales Narrative. What is the probability that no sales are made?

Question 18

Driver Education Narrative
Three randomly chosen 14-year-old middle school students who had not yet taken driver's education classes were given the written part of the Manitoba Driver's Exam. Each student was graded as passing (P) or failing (F) the written exam.
Refer to Driver Education Narrative. Assuming each combination in the sample space is equally likely, what is the probability that all three students fail?

Question 19

SALES NARRATIVE
A salesperson either makes a sale (S) or does not make a sale (N) with each of two potential customers. The simple events and their probabilities are given below.
Refer to Sales Narrative. What is the probability that at least one sale is made?

Question 20

Driver Education Narrative
Three randomly chosen 14-year-old middle school students who had not yet taken driver's education classes were given the written part of the Manitoba Driver's Exam. Each student was graded as passing (P) or failing (F) the written exam.
Refer to Driver Education Narrative. Assuming each combination in the sample space is equally likely, what is the probability at least one student passes the written test?

Question 21

A professor has received a grant to travel to an archaeological dig site. The grant includes funds for three graduate students to accompany the professor. If there are six graduate students available to the professor and all the funds are to be used (i.e., three students will go), how many choices does the professor have?

Question 22

An Italian restaurant in Québec City offers a special summer menu in which, for a fixed dinner cost, you can choose from one of two salads, one of three entrees, and one of four desserts. How many different dinners are available?

Question 23

Smoking Habits of Health Club Members Narrative
A group of 40 people at a health club were classified according to their gender and smoking habits, as shown in the table below. One person is selected at random from that group of 40 people.
Smoking Habits
Refer to Smoking Habits of Health Club Members Narrative. What is the probability the person is female and does not smoke?

Question 24

Smoking Habits of Health Club Members Narrative
A group of 40 people at a health club were classified according to their gender and smoking habits, as shown in the table below. One person is selected at random from that group of 40 people.
Smoking Habits
Refer to Smoking Habits of Health Club Members Narrative. If the person is female, what is the probability she does not smoke?

Question 25

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. What is the probability that the randomly selected shopper is under 25 years of age?

Question 26

Smoking Habits of Health Club Members Narrative
A group of 40 people at a health club were classified according to their gender and smoking habits, as shown in the table below. One person is selected at random from that group of 40 people.
Smoking Habits
Refer to Smoking Habits of Health Club Members Narrative. What is the probability the person is male?

Question 27

Smoking Habits of Health Club Members Narrative
A group of 40 people at a health club were classified according to their gender and smoking habits, as shown in the table below. One person is selected at random from that group of 40 people.
Smoking Habits
Refer to Smoking Habits of Health Club Members Narrative. What is the probability the person smokes?

Question 28

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. Convert the frequency table shown above into a probability table.

Question 29

Smoking Habits of Health Club Members Narrative
A group of 40 people at a health club were classified according to their gender and smoking habits, as shown in the table below. One person is selected at random from that group of 40 people.
Smoking Habits
Refer to Smoking Habits of Health Club Members Narrative. What is the probability the person is female?

Question 30

An interior decorator must furnish two offices. Each office must have a desk, a chair, a file cabinet, and two bookcases. At a local office furniture store there are 6 models of desks, 8 models of chairs, 4 models of file cabinets, and 10 models of bookcases, all of which are compatible. (Any desk can be matched with any chair, etc.) How many choices does the decorator have if he wants to select 2 desks, 2 chairs, 2 file cabinets, and 4 bookcases but he doesn't want to select more than one of any model?

Question 31

Coffee Brands Narrative
A food company plans to conduct an experiment to compare its brand of coffee with that of two competitors. A single person is hired to taste each of three brands of coffee, which are unmarked except for identifying symbols, A, B, and C.
Refer to Coffee Brands Narrative. List the simple events in the sample space S.

Question 32

Heidi prepares for an exam by studying a list of 15 s. She can solve 9 of them. For the exam, the instructor selects 7 questions at random from the list of 15. What is the probability that Heidi can solve all 7 s on the exam?

Question 33

Smoking Habits of Health Club Members Narrative
A group of 40 people at a health club were classified according to their gender and smoking habits, as shown in the table below. One person is selected at random from that group of 40 people.
Smoking Habits
Refer to Smoking Habits of Health Club Members Narrative. If the person is male, what is the probability he smokes?

Question 34

Smoking Habits of Health Club Members Narrative
A group of 40 people at a health club were classified according to their gender and smoking habits, as shown in the table below. One person is selected at random from that group of 40 people.
Smoking Habits
Refer to Smoking Habits of Health Club Members Narrative. What is the probability the person does not smoke?

Question 35

Coffee Brands Narrative
A food company plans to conduct an experiment to compare its brand of coffee with that of two competitors. A single person is hired to taste each of three brands of coffee, which are unmarked except for identifying symbols, A, B, and C.
Refer to Coffee Brands Narrative. If the taster has no ability to distinguish difference in taste among coffees, what is the probability that the taster will rank coffee type C as the most desirable? As the least desirable?

Question 36

Smoking Habits of Health Club Members Narrative
A group of 40 people at a health club were classified according to their gender and smoking habits, as shown in the table below. One person is selected at random from that group of 40 people.
Smoking Habits
Refer to Smoking Habits of Health Club Members Narrative. What is the probability the person is male and smokes?

Question 37

How many permutations of 3 colours can be drawn from a group of 20 colours?

Question 38

A businessman in Hamilton is preparing an itinerary for a visit to five major cities. Each city will be visited once and only once. The distance travelled, and hence the cost of the trip, will depend on the order in which he plans his route. How many different itineraries (and trip costs) are possible?

Question 39

A graduate student has decided she needs a day at the beach. She will need a swimsuit, a pair of sunglasses, and a beach towel for the occasion. If she has two swimsuits, three pairs of sunglasses, and five beach towels, how many different choices does she have?

Question 40

How many different combinations of 5 students can be drawn from a class of 25 students?

Question 41

Psychological Tests Narrative
A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50.
Refer to Psychological Tests Narrative. If the randomly selected student does well on the number pattern recognition test, what is the probability he or she will also do well on the word association test?

Question 42

Salary of Working Mothers Narrative
A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following probability table:
Number of Children Let A denote the event that a working woman has two or fewer children, and let B denote the event that a working woman has a low salary.
Refer to Salary of Working Mothers Narrative. What is the probability that a working woman either has two or fewer children or has a low salary?

Question 43

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. What is the probability that the randomly selected shopper is either female or over 40 years of age?

Question 44

Salary of Working Mothers Narrative
A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following probability table:
Number of Children Let A denote the event that a working woman has two or fewer children, and let B denote the event that a working woman has a low salary.
Refer to Salary of Working Mothers Narrative. What is the probability that a working woman has a low salary?

Question 45

Psychological Tests Narrative
A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50.
Refer to Psychological Tests Narrative. Are the events W and N mutually exclusive? Justify your ANS.

Question 46

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. If the randomly selected shopper is male, what is the probability he is under 25 years of age?

Question 47

Psychological Tests Narrative
A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50.
Studies have shown a particular television commercial is understood by 25% of Grade 1 students and 80% of Grade 4 students. If a television advertising agency randomly selects one Grade 1 and one Grade 4 student, what is the probability neither child would understand the commercial, assuming the children's reactions are independent?

Question 48

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. If the randomly selected shopper is under 25 years of age, what is the probability that the shopper is male?

Question 49

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. Are the gender of the shopper and the shopper's age independent events? Explain.

Question 50

Psychological Tests Narrative
A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50.
Refer to Psychological Tests Narrative. Are the events W and N independent? Explain.

Question 51

Salary of Working Mothers Narrative
A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following probability table:
Number of Children Let A denote the event that a working woman has two or fewer children, and let B denote the event that a working woman has a low salary.
Refer to Salary of Working Mothers Narrative. What is the probability that a working woman has two or fewer children and has a low salary?

Question 52

Psychological Tests Narrative
A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50.
Refer to Psychological Tests Narrative. What is the probability that the randomly selected student does well on the number pattern recognition test?

Question 53

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. Are the gender of the shopper and the shopper's age mutually exclusive events? Explain.

Question 54

Psychological Tests Narrative
A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50.
Refer to Psychological Tests Narrative. What is the probability that the randomly selected student does well on the word association test?

Question 55

Salary of Working Mothers Narrative
A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following probability table:
Number of Children Let A denote the event that a working woman has two or fewer children, and let B denote the event that a working woman has a low salary.
Refer to Salary of Working Mothers Narrative. What is the probability that a working woman has two or fewer children?

Question 56

Psychological Tests Narrative
A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50.
Refer to Psychological Tests Narrative. If the randomly selected student does well on the word association test, what is the probability he or she will also do well on the number pattern recognition test?

Question 57

Psychological Tests Narrative
A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50.
Refer to Psychological Tests Narrative. What is the probability that the randomly selected student does well on at least one of the tests?

Question 58

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. What is the probability that the randomly selected shopper is male and under 25 years of age?

Question 59

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. If the randomly selected shopper is female, what is the probability that she is 25 to 40 years old?

Question 60

Mall Shopper Narrative
One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers.
Age Group
Refer to Mall Shopper Narrative. What is the probability that the randomly selected shopper is male?

Question 61

Late Night Talk Shows Narrative
Let A be the event that a randomly selected person watches the Tonight Show with Jay Leno (event A) and B be the event that a randomly selected person watches the Late Show with David Letterman (event B). It is possible to time-shift a program to a more convenient hour and thus watch both programs. Suppose the following probabilities are given: P(A B) = 0.20, P(A ) = 0.40, P( ) = 0.10, and P( ) = 0.30.
Refer to Late Night Talk Shows Narrative. What is the probability that a randomly selected person watches only David Letterman?

Question 62

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Find P .

Question 63

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Find the probability of B given that A has occurred.

Question 64

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Are events A and B independent? Explain.

Question 65

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Find P(A B).

Question 66

Late Night Talk Shows Narrative
Let A be the event that a randomly selected person watches the Tonight Show with Jay Leno (event A) and B be the event that a randomly selected person watches the Late Show with David Letterman (event B). It is possible to time-shift a program to a more convenient hour and thus watch both programs. Suppose the following probabilities are given: P(A B) = 0.20, P(A ) = 0.40, P( ) = 0.10, and P( ) = 0.30.
Refer to Late Night Talk Shows Narrative. What is the probability that a randomly selected person watches both shows?

Question 67

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Find the probability of A given that B has occurred.

Question 68

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Find P(B).

Question 69

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Find P(A).

Question 70

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Find P( ).

Question 71

Late Night Talk Shows Narrative
Let A be the event that a randomly selected person watches the Tonight Show with Jay Leno (event A) and B be the event that a randomly selected person watches the Late Show with David Letterman (event B). It is possible to time-shift a program to a more convenient hour and thus watch both programs. Suppose the following probabilities are given: P(A B) = 0.20, P(A ) = 0.40, P( ) = 0.10, and P( ) = 0.30.
Refer to Late Night Talk Shows Narrative. What is the probability that a randomly selected person watches only Jay Leno?

Question 72

Salary of Working Mothers Narrative
A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following probability table:
Number of Children Let A denote the event that a working woman has two or fewer children, and let B denote the event that a working woman has a low salary.
Refer to Salary of Working Mothers Narrative. If a working woman has two or fewer children, what is the probability that she has a low salary?

Question 73

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
A missile designed to destroy enemy satellites has a 0.80 chance of destroying its target. If the government tests three missiles by firing them at a target, what is the probability all three fail to destroy the target? (Assume the missiles perform independently.)

Question 74

Late Night Talk Shows Narrative
Let A be the event that a randomly selected person watches the Tonight Show with Jay Leno (event A) and B be the event that a randomly selected person watches the Late Show with David Letterman (event B). It is possible to time-shift a program to a more convenient hour and thus watch both programs. Suppose the following probabilities are given: P(A B) = 0.20, P(A ) = 0.40, P( ) = 0.10, and P( ) = 0.30.
Refer to Late Night Talk Shows Narrative. What is the probability that a randomly selected person watches Jay Leno?

Question 75

Salary of Working Mothers Narrative
A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following probability table:
Number of Children Let A denote the event that a working woman has two or fewer children, and let B denote the event that a working woman has a low salary.
Refer to Salary of Working Mothers Narrative. From this information, can one conclude that the salary of a working woman with school-aged children and the number of children she has are independent events? Explain.

Question 76

Late Night Talk Shows Narrative
Let A be the event that a randomly selected person watches the Tonight Show with Jay Leno (event A) and B be the event that a randomly selected person watches the Late Show with David Letterman (event B). It is possible to time-shift a program to a more convenient hour and thus watch both programs. Suppose the following probabilities are given: P(A B) = 0.20, P(A ) = 0.40, P( ) = 0.10, and P( ) = 0.30.
Refer to Late Night Talk Shows Narrative. If we know a person watches Jay Leno, what is the probability he or she also watches David Letterman?

Question 77

Salary of Working Mothers Narrative
A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following probability table:
Number of Children Let A denote the event that a working woman has two or fewer children, and let B denote the event that a working woman has a low salary.
Refer to Salary of Working Mothers Narrative. If a working woman has a low salary, what is the probability that she has two or fewer children?

Question 78

Late Night Talk Shows Narrative
Let A be the event that a randomly selected person watches the Tonight Show with Jay Leno (event A) and B be the event that a randomly selected person watches the Late Show with David Letterman (event B). It is possible to time-shift a program to a more convenient hour and thus watch both programs. Suppose the following probabilities are given: P(A B) = 0.20, P(A ) = 0.40, P( ) = 0.10, and P( ) = 0.30.
Refer to Late Night Talk Shows Narrative. What is the probability that a randomly selected person watches David Letterman?

Question 79

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Find P(A B).

Question 80

Drug Offenders Narrative
Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below:
Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest:
A: The offender has 10 or more years of education.
B: The offender is convicted within two years after completion of treatment.
Refer to Drug Offenders Narrative. Find P .