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Exam 4: Introduction to Probability

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Question 21

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The results of a survey of 800 married couples and the number of children they had is shown below. $\begin{array}{ll}\text { Number of Children }&\text { Probability }\\0 & 0.050 \\1 & 0.125 \\2 & 0.600 \\3 & 0.150 \\4 & 0.050 \\5 & 0025\end{array}$ 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?

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a. 0.925
b...

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Question 22

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If A and B are independent events with PA) = 0.65 and PA ∩ B) = 0.26, then, PB) =

A) 0.400
B) 0.169
C) 0.390
D) 0.650

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

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Question 23

Multiple Choice

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If PA∪B) = 0.87 and PA∩B) = 0.00, then PB) = ?

The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed 2 times and event A did not occur, then on the third trial event A

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

If PA) = 0.4, PB | A) = 0.35, PA ∪ B) = 0.69, then PB) =

Eight individuals are candidates for positions of president, vice president, and treasurer of an organization. How many possibilities of selections exist?

If PA) = 0.5 and PB) = 0.5, then PA ∩ B)

If a dime is tossed four times and comes up tails all four times, the probability of heads on the fifth trial is

Records of a company show that 15% of the employees have only a high school diploma; 75% have bachelor degrees; and 10% have graduate degrees. Of those with only a high school diploma, 12% hold management positions; whereas, of those having bachelor degrees, 58% hold management positions. Finally, 82% of the employees who have graduate degrees hold management positions. a. What percentage of employees holds management positions? b. Given that a person holds a management position, what is the probability that she/he has a graduate degree?

The following table shows the number of students in three different degree programs and whether they are graduate or undergraduate students: $\begin{array} { l | r r | r } & \text { Under graduate } & \text { Graduate } & \text { Total } \\\hline \text { Business } & 150 & 50 & 200 \\\text { Engineering } & 150 & 25 & 175 \\\text { Arts \& Sciences } & 100 & 25 & 125 \\\hline \text { Total } & 400 & 100 & 500\end{array}$ a. What is the probability that a randomly selected student is an undergraduate? b. What percentage of students is engineering majors? c. If we know that a selected student is an undergraduate, what is the probability that he or she is a business major? d. A student is enrolled in the Arts and Sciences school. What is the probability that the student is an undergraduate student? e. What is the probability that a randomly selected student is a graduate Business major?

Records of a company show that 20% of the employees have only a high school diploma; 70% have bachelor degrees; and 10% have graduate degrees. Of those with only a high school diploma, 10% hold management positions; whereas, of those having bachelor degrees, 40% hold management positions. Finally, 80% of the employees who have graduate degrees hold management positions. a. What percentage of employees holds management positions? b. Given that a person holds a management position, what is the probability that she/he has a graduate degree?

A statistics professor has noted from past experience that a student who follows a program of studying two hours for each hour in class has a probability of 0.9 of getting a grade of C or better, while a student who does not follow a regular study program has a probability of 0.2 of getting a C or better. It is known that 70% of the students follow the study program. Find the probability that a student who has earned a C or better grade, followed the program.

If PA) = 0.58, PB) = 0.44, and PA ∩ B) = 0.25, then PA ∪ B) =

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

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. $\begin{array}{l|rr|r} & \text { Men } & \text { Women } & \text { Total } \\\hline \text { In Favor } & 1,400 & 280 & 1,680 \\\text { Opposed } & 840 & 3,080 & 3,920\\\hline \text { Total } & 2,240 & 3,360 & 5,600\end{array}$ Let: M be the event a resident is a man W be the event a resident is a woman F be the event a resident is in favor P be the event a resident is opposed 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.

In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55. The probability that UTC will defeat both opponents is 0.3465. a. What is the probability that UTC will defeat Furman given that they defeat Marshall? b. What is the probability that UTC will win at least one of the games? c. What is the probability of UTC winning both games? d. Are the outcomes of the games independent? Explain and substantiate your answer.

Of five letters A, B, C, D, and E) , two letters are to be selected at random. How many possible selections are there?

A method of assigning probabilities based upon judgment is referred to as the

Events that have no sample points in common are