Exam 4: B: probability and Probability Distributions

Typists' Errors Narrative The random variable x is defined as the number of mistakes made by a typist on a randomly chosen page of a physics thesis. The probability distribution follows: -Refer to Typists' Errors Narrative. Find P(0 x < 2).

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).

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?

Hand Soap Product Narrative A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help judge the success of the new product. The survey showed 40% of the consumers had seen an advertisement for the new soap, 20% had tried the new soap, and 15% had both seen an advertisement and tried the new soap. Let event A denote that the consumers had seen an ad for the new soap, and event B denote that the consumers had tried the new soap. -Refer to Hand Soap Product Narrative. What is the probability a randomly selected consumer had either seen an advertisement or tried the new soap?

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).

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(D | C).

Defective Bolts Narrative Approximately 5% of the bolts coming off a production line have serious defects. Two bolts are randomly selected for inspection. -Refer to Defective Bolts Narrative. Find .

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?

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 either single or over 40 years of age?

Hand Soap Product Narrative A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help judge the success of the new product. The survey showed 40% of the consumers had seen an advertisement for the new soap, 20% had tried the new soap, and 15% had both seen an advertisement and tried the new soap. Let event A denote that the consumers had seen an ad for the new soap, and event B denote that the consumers had tried the new soap. -Refer to Hand Soap Product Narrative. If a randomly chosen consumer has seen an advertisement for the new soap, what is the probability he or she has tried the product?

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?

Number of Cars Narrative Let the random variable x represent the number of cars owned by a family. Assume that x can take on five values: 0, 1, 2, 3, 4. A partial probability distribution is shown below: -Refer to Number of Cars Narrative. Construct a probability histogram for p(x).

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( )?

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?

Number of Cars Narrative Let the random variable x represent the number of cars owned by a family. Assume that x can take on five values: 0, 1, 2, 3, 4. A partial probability distribution is shown below: -Refer to Number of Cars Narrative. Find the probability that a family owns one to three cars, inclusive.

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. After breaking the bank at the casino playing this card game, you decide to open your own casino where the customers can play your favourite card game. How much should you charge the players if you want to have an average profit of $1 per play?

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 either a smoker or a female or both.

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.

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?

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?