Exam 7: Probability

Use the following information for questions: A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and one male assistant (Josh). Each TA teaches one discussion section. -A student picks a discussion section. The events L = {the TA is Lauren} and R = {the TA is Rona} are

Use the following information for questions: A mail-order company classifies its customers by gender (male/female) and by location of residence (urban/suburban). The market research department has determined that 2/3 of their customers are female and that 75% of their customers live in the suburbs. They have also determined that gender and location of residence seem to be independent of one another. -The mail order company will randomly select one of their customers. Suppose we know they have selected a person in the suburbs. What is the probability that this person is female?

Students at a university who apply for campus housing can be assigned to live in a dormitory room, a suite in a dormitory or an apartment. If Alice has a 0.30 chance of being assigned to a dormitory room and a 0.50 chance of being assigned to a suite in a dormitory, what is the probability that she will be assigned to an apartment?

Use the following information for questions: For each of the following statements, determine if they are true or false. -The probability of the intersection of two events A and B, and the probability of the union of A and B can never be equal.

A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next. What is the probability that a customer must open three or more bottles before winning a prize?

Use the following information for questions: In the Banana Republic there are two producers of PCs, referred to as Pac and Bell. Assume that there are no PC imports. The market shares for these two producers are 70% for Pac and 30% for Bell. One executive at Bell proposes a longer warranty period (similar to one given by auto makers) to be offered at a slight extra cost as a plan to increase market share. A market research company appointed by Bell conducts a census of PC owners on their opinion of this warranty proposal. Among owners of a PC made by Pac, 50% like the proposal, 30% are indifferent to it, while the remaining owners oppose it. Among owners of a PC made by Bell, 70% like the proposal, 20% are indifferent to it, and the remaining owners oppose it. -A PC owner will be selected at random. What is the probability that the person will own a PC made by Bell?

Use the following information for questions: A study was conducted at a small college on first-year students living on campus. A number of variables were measured. The table below provides information regarding number of roommates and end of term health status for the first-year students at this college. Health status for individuals is measured as poor, average, and exceptional. -Are the events H = {the student has poor health status} and N = {the student has no roommates} mutually exclusive?

A plane flies over the ocean in search of schools of fish. On any given day, there is a 0.07 chance of finding 2 or more schools of fish, and a 0.28 chance of finding only one school of fish. What is the chance the day of searching results in not finding any schools of fish at all?

A short quiz has two true-false questions and one multiple-choice question with four choices. A student guesses at each question. Assuming the choices are all equally likely, what is the probability that the student gets all three correct?

A survey was given to sophomores at a university and one of the questions asked was "What is the probability that you will leave school before you graduate?"The answer to this question for an individual student is an example of

A test to detect prostate cancer in men has a specificity of 80%. This means that

If events A and B are mutually exclusive (disjoint) then

Use the following information for questions: For each situation, decide if the probability described is a subjective (personal) probability or a relative frequency probability. -A football fan believes that the Oakland Raiders have a 50% chance of winning the next Super bowl. The 50% is a

Use the following information for questions: The following table provides information regarding health status and smoking status of residents of a small community (health status for individuals was measured by the number of visits to the hospital during the year). -Are the events N = {the resident does not smoke} and Z = {the resident made zero visits to the hospital} independent?

Use the following information for questions: Thirty percent of the students in a high school face a disciplinary action of some kind before they graduate. Of those students, 40% go on to college. Of the 70% who do not face a disciplinary action, 60% go on to college. -Given that a randomly selected student goes on to college, what is the probability that he or she faced a disciplinary action?

Use the following information for questions: In a survey of 1000 adults, respondents were asked about the expense of a college education and the relative necessity of financial assistance. The correspondents were classified as to whether they currently had a child in college or not (college status), and whether they thought the loan obligation for most college students was too high, about right, or too little (loan obligation opinion). The table below summarizes some of the survey results. Use these results to answer the following questions. -Are the events H = {the adult thinks loan obligations are too high} and C = {the adult has a child in college} independent?

Use the following information for questions: Suppose two different states each pick a two-digit lottery number between 00 and 99 (for a 100 possible numbers). -What is the probability that both states pick the number 13?

Consider the following three sequences of outcomes after tossing 6 coins: HHHHHH, HHHTTT, and HTHHTH. Which of the following represents the ordering of these three sequences in order of highest to lowest probability?

Use the following information for questions: A mail-order company classifies its customers by gender (male/female) and by location of residence (urban/suburban). The market research department has determined that 2/3 of their customers are female and that 75% of their customers live in the suburbs. They have also determined that gender and location of residence seem to be independent of one another. -If the mail order company will randomly select one of their customers, what is the probability that it will be a suburban female?

Use the following information for questions: The following table provides information regarding health status and smoking status of residents of a small community (health status for individuals was measured by the number of visits to the hospital during the year). -What is the probability that a randomly selected resident made zero visits to the hospital?