Exam 4: Probability and Probability Models

Suppose that A₁, A₂, and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7, P(A₂) = .3, P(B│A₁) = .2, P(B│A₂) = .4. Find P(A₁│B).

A card is drawn from a standard deck. What is the probability the card is an ace, given that it is a club?

Independently, a coin is tossed, a card is drawn from a deck, and a die is thrown. What is the probability of observing a head on the coin, an ace on the card, and a five on the die?

Suppose that you believe that the probability you will get a grade of B or better in Introduction to Finance is .6 and the probability that you will get a grade of B or better in Introduction to Accounting is .5. If these events are independent, what is the probability that you will receive a grade of B or better in both courses?

A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is a Democrat or a Republican.

It is very common for a television series to draw a large audience for special events or for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2 percent of all US TV households. Suppose that three TV households are randomly selected. What is the probability that all three households viewed this special show?

If P(A|B) = .2 and P(B) = .8, determine the intersection of events A and B.

A report on high school graduation stated that 85 percent of high school students graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that exactly one of the three graduates?

Events that have no sample space outcomes in common, and therefore cannot occur simultaneously, are referred to as independent events.

A television program director has 14 shows available for Monday night but can choose only 5 shows. How many different possible combinations are there?

Probabilities must be assigned to each sample space outcome so that the probabilities of all the sample space outcomes add up to ________.

If events A and B are independent, then the probability of simultaneous occurrence of event A and event B can be found with ________.

A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is a male Republican.

In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all males belong to a Greek organization. What is the probability that an undergraduate is in a Greek organization, given that the undergraduate is a female?

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 male and has a favorable opinion.

What is the probability that any two people chosen at random were born on the same day of the week?

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is female or works as a member of the faculty?

The probability of an event is the sum of the probabilities of the sample space outcomes that correspond to the event.

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is a member of the faculty?

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 an Average score?