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. If Lily goes to a fast-food restaurant and orders french fries, what is the probability that she is at a Burger King?

Smoking and Gender Narrative An experiment can result in one or both of events A = Smoker and B = Female, with the joint probabilities shown in the table below. A person is selected at random. -Refer to Smoking and Gender Narrative. Are smoking and gender of the person independent events? Explain.

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

Working mothers in Canada Statistics Canada wanted to find the distribution of ages of working women living in Canada who were single mothers. The researcher drew a random sample of some 300 families from the government tax records and found the following distribution: Age Group One family was selected at random from tax base records of families with working mothers. -Refer to Working mothers in Canada. What is the probability that the randomly selected working mother is single and under 25 years of age?

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?

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?

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.

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 D).

Smoking and Gender Narrative An experiment can result in one or both of events A = Smoker and B = Female, with the joint probabilities shown in the table below. A person is selected at random. -Refer to Smoking and Gender Narrative. Find the probability that the person is a female, given that she smokes.

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?

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( )?

Casino Card Game Narrative The probability distribution of your winnings at a casino's card game is shown below. -Refer to Casino Card Game Narrative. What is the chance you win more than $1 if you play just once?

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?

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?

College in Ontario Narrative A college in Ontario has 1000 employees. Four hundred of the employees have at least 20 years of experience (event A); 100 of the employees were born in Ontario (event B); and 300 of the employees had a background in Microsoft Office 2003 (event C). Assume events A, B, and C are independent. -Refer to College in Ontario Narrative. What is the probability of finding an employee who meets at least two of the three criteria?

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?

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?

College in Ontario Narrative A college in Ontario has 1000 employees. Four hundred of the employees have at least 20 years of experience (event A); 100 of the employees were born in Ontario (event B); and 300 of the employees had a background in Microsoft Office 2003 (event C). Assume events A, B, and C are independent. -Refer to College in Ontario Narrative. What is the probability of finding an employee who meets all three of these criteria?

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

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?