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Exam 4: Introduction to Probability

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Question 21

Multiple Choice

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The addition law is potentially helpful when we are interested in computing the probability of

A) independent events
B) the intersection of two events
C) the union of two events
D) conditional events

E) A) and B)
F) A) and C)

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Question 22

Multiple Choice

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If P(A) = 0.58, P(B) = 0.44, and P(A $\cap$ B) = 0.25, then P(A $\cup$ B) =

A) 1.02
B) 0.77
C) 0.11
D) 0.39

E) B) and C)
F) A) and D)

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Question 23

Short Answer

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Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 65% of those students who use the lab on a regular basis make a grade of A in the course. On the other hand, only 10% of students who do not go to the lab on a regular basis make a grade of A. If a particular student made an A, determine the probability that she or he used the lab on a regular basis.

From among 8 students how many committees consisting of 3 students can be selected?

From a group of three finalists for a privately endowed scholarship, two individuals are to be selected for the first and second places. Determine the number of possible selections.

Some of the CDs produced by a manufacturer are defective. From the production line, 5 CDs are selected and inspected. How many sample points exist in this experiment?

A small town has 5,600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents' responses, broken down by sex. a. Find the joint probability table. b. Find the marginal probabilities. c. What is the probability that a randomly selected resident is a man and is in favor of building the bridge? d. What is the probability that a randomly selected resident is a man? e. What is the probability that a randomly selected resident is in favor of building the bridge? f. What is the probability that a randomly selected resident is a man or in favor of building the bridge? g. A randomly selected resident turns out to be male. Compute the probability that he is in favor of building the bridge.

On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and "cold" weather is .15. Are snow and "cold" weather independent events?

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is

Sixty percent of the student body at UTC is from the state of Tennessee (T), 30% percent are from other states (O), and the remainder are international students (I). Twenty percent of students from Tennessee live in the dormitories, whereas, 50% of students from other states live in the dormitories. Finally, 80% of the international students live in the dormitories. a.What percentage of UTC students live in the dormitories? b.Given that a student lives in the dormitory, what is the probability that she/he is an international student? c.Given that a student lives in the dormitory, what is the probability that she/he is from Tennessee?

How many committees, consisting of 3 female and 5 male students, can be selected from a group of 5 female and 8 male students?

From a group of seven finalists to a contest, three individuals are to be selected for the first and second and third places. Determine the number of possible selections.

Assume that each year the IRS randomly audits 10% of the tax returns. If a married couple has filed separate returns, a.What is the probability that both the husband and the wife will be audited? b.What is the probability that only one of them will be audited? c.What is the probability that neither one of them will be audited? d.What is the probability that at least one of them will be audited?

In a horse race, nine horses are running. Assume you have purchased a Trifecta ticket. (In Trifecta, the player selects three horses as first, second, and third place winners. To win, those three horses must finish the race in the precise order the player has selected.) How many possibilities of a Trifecta exist?

Assume your favorite football team has 3 games left to finish the season. The outcome of each game can be win, lose, or tie. How many possible outcomes exist?

The union of two events with nonzero probabilities

If a six sided die is tossed two times, the probability of obtaining two "4s" in a row is

A perfectly balanced coin is tossed 6 times and tails appears on all six tosses. Then, on the seventh trial

An experiment consists of four outcomes with P(E₁) = 0.2, P(E₂) = 0.3, and P(E₃) = 0.4. The probability of outcome E₄ is

The results of a survey of 800 married couples and the number of children they had is shown below. If a couple is selected at random, what is the probability that the couple will have a.Less than 4 children? b.More than 2 children? c.Either 2 or 3 children?