Exam 4: Probability and Probability Models

A(n) ________ is a collection of sample space outcomes.

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. Of the applicants with similar qualities, only 10 percent are accepted into both University A and University B. Is the acceptance decision at University A independent of the acceptance decision at University B?

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If a student has received a grade of C, what is the probability that the student is male?

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are A and N mutually exclusive?

Suppose the probability that an individual has a particular medical condition is .10. Tests of an individual's DNA can determine whether they have this medical condition but with only an 85 percent accuracy rate (that is, if the condition is present, the probability that the DNA test will give a positive finding is .85). If the medical condition is not present, the probability of the DNA test saying the medical condition exists is 0.03. What is the probability that the medical condition is present if the DNA test comes back positive?

What is the probability of rolling a seven with a pair of fair dice?

Every current applicant for a position in the marketing department of Company A is given a 10-question test on interpretation of findings from statistical analyses. Individuals are rated on three levels based on their scores: Excellent (9-10 correct), Average (5-8 correct), and Poor (fewer than 5 correct). Historically, the probability of an individual scoring Excellent = .38, Average = .52, and Poor = .10. Also, the company knows that 90 percent of applicants who score Excellent are offered a position, 75 percent of applicants who score Average are offered a position, and 35 percent of the applicants who score Poor are offered a position. What is the probability that an individual who is offered a position has a Poor score?

An event is a collection of sample space outcomes.

The set of all possible outcomes for an experiment is called a(n) ________.

In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan. Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable responses, 15 were males. If one citizen is randomly selected, find the probability that person is female or has an unfavorable opinion.

The probability of event A occurring given that event B has already occurred is 0.61. The probability of both events occurring is 0.5. What is the probability of event B occurring?

In any probability situation, either an event or its complement must occur.

Determine whether these two events are mutually exclusive: someone born in the United States and a U.S. citizen.

There are two types of probability distributions: discrete and binomial.

If we consider the toss of four coins as an experiment, how many outcomes does the sample space consist of?

Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer neither buys beer nor buys cigars.

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If a student is male, what is the probability he is a C student?

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that only one of the items is defective?

When the probability of one event is influenced by whether or not another event occurs, the events are said to be ________.

A card is drawn from a standard deck. Given that a face card is drawn, what is the probability it will be a king?