Exam 4: B: probability and Probability Distributions

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 three cars.

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. What is the probability that at least two of the three Dell computer users would buy another Dell computer?

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?

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 the probability distribution for x, the number of defective bolts in the sample.

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 .

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 mutually exclusive events? Explain.

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(x < 1).

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. -There are four different kinds of radar systems designed to detect or monitor the airspace around a major airport for high-flying objects, low-flying objects, runway traffic, and wind shear. Each operates independently from the others. If each system has probability 0.90 of functioning correctly, find the probability at least one radar system will fail.

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?

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 under 25 years of age?

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 smoker.

Suppose that P(A) = 0.6, P(B) = 0.7, and that events A and B are independent. a. Find P(A B). b. Find P(A B). c. Find P(A/B). d. Find P(B/A).

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).

Steve takes either a bus or the subway to go to work, with probabilities 0.25 and 0.75, respectively. When he takes the bus, he is late 40% of the time. When he takes the subway, he is late 30% of the time. If Steve is late for work on a particular day, what is the probability that he took the bus?

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?

Waste Management Project Narrative A federal agency is trying to decide which of two waste management projects to investigate as the source of air pollution. In the past, projects of the first type were in violation of air quality standards with probability 0.3 on any given day, while projects of the second type were in violation of air quality standards with probability 0.25 on any given day. It is not possible for both projects to pollute the air in one day. Let , i = 1, 2, denote that project of type i was in violation of air quality standards. -Refer to Waste Management Project Narrative. Find the probability of an air pollution being caused by either the first project or the second project.

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

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. What is E(x)?

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. If the person is female, find the probability that she is a smoker.

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. Convert the frequency table shown above into a probability distribution.