Exam 4: B: probability and Probability Distributions

Fast-Food Restaurants Narrative Lily frequents one of two fast-food restaurants, choosing McDonald's 25% of the time and Burger King 75% of the time. Regardless of where she goes, she buys french fries on 60% of her visits. -Refer to Fast-Food Restaurants Narrative. Are the two events in the previous question independent? Explain.

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?

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.

At a local pet adoption centre for dogs and cats, it is known that if a person adopts a pet, there is a 0.45 probability that it will be a cat and a 0.55 probability that it will be a dog. If a cat is adopted, the probability that it is female is 0.60. If a dog is adopted, the probability that it is female is 0.35. An adopted pet is selected at random and is found to be male. What is the probability that the adopted pet is a dog?

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?

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?

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?

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.

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).

City Council Election Narrative An election is being held to fill two city council seats. Two fiscally conservative candidates (denoted by C) and three small-L liberal candidates (denoted by L) are running for office. Assume the candidates are equally likely to be elected, and independent of each other. -Refer to City Council Election Narrative. What is the probability one Conservative and one Liberal are elected to the two city council seats?

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?

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?

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?

Dell Computer Owners Narrative Dell computer owners are very faithful. Despite reporting s with their current systems, 90% of Dell owners said they would buy another computer from the company, based on the service they received. Suppose you randomly select three current Dell computer users and ask them whether they would buy another Dell computer system. -Refer to Dell Computer Owners Narrative. Construct the probability histogram for p(x).

Random Selection of Marbles Narrative A box contains one red, three blue, and two green marbles. Two marbles are randomly selected without replacement. Define events R, B, G, C, and D as follows: R = {The selected marble is red.} B = {The selected marble is blue.} G = {The selected marble is green.} C = {Both marbles selected are the same colour.} D = {At least one of the marbles is blue.} -Refer to Random Selection of Marbles Narrative. Find P(C).

Medical case histories indicate that different illnesses may produce identical symptoms. Suppose a particular set of symptoms, which we will denote as event H, occurs only when any one of these illnesses, A, B, or C, occurs. (For the sake of simplicity, we will assume that illnesses A, B, and C are mutually exclusive.) Studies show the probabilities of getting the three illnesses are as follows: P(A) = 0.015, P(B) = 0.005, and P(C) = 0.025. The probabilities of developing the symptoms H, given a specific illness, are P(H/A) = 0.85, P(H/B) = 0.90, and P(H/C) = 0.70. Assuming that an ill person shows the symptoms H, what is the probability that the person has illness A?

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?

Weight Gain for Calves Narrative Let x denote the weight gain in kilograms per month for a calf. The probability distribution of x is shown below. -Refer to Weight Gain for Calves Narrative. What is P(x 10)?

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?

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.