Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A)  0.14 
B)  0.43 
C)  0.75 
D)  0.59 
A)  0.14 
B)  0.43 
C)  0.75 
D)  0.59

Question 3

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?

Accepted Answer

The answer of Records of a company show that 20%...

Question 4

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?

Accepted Answer

The answer of Records of a company show that 15%...

Question 5

Events that have no sample points in common are

Accepted Answer

A)  independent events 
B)  posterior events 
C)  mutually exclusive events 
D)  complements 
A)  independent events 
B)  posterior events 
C)  mutually exclusive events 
D)  complements

Question 6

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

Accepted Answer

A)  smaller than the probability of tails 
B)  larger than the probability of tails 
C)  1/2 
D)  1/32 
A)  smaller than the probability of tails 
B)  larger than the probability of tails 
C)  1/2 
D)  1/32

Question 7

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?

Accepted Answer

a. 0.925
b

Question 8

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?

Accepted Answer

a. 0.8
b.

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

A)  must occur 
B)  may occur 
C)  could not occur 
D)  has a 2/3 probability of occurring 
A)  must occur 
B)  may occur 
C)  could not occur 
D)  has a 2/3 probability of occurring

Question 11

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

Accepted Answer

A)  20 
B)  7 
C)  5! 
D)  10 
A)  20 
B)  7 
C)  5! 
D)  10

Question 12

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

Accepted Answer

A)  is 0.00 
B)  is 1.00 
C)  is 0.5 
D)  None of these alternatives is correct. 
A)  is 0.00 
B)  is 1.00 
C)  is 0.5 
D)  None of these alternatives is correct.

Question 13

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

Accepted Answer

A)  there is not sufficient information to answer this question 
B)  0.00 
C)  0.13 
D)  larger than 1 
A)  there is not sufficient information to answer this question 
B)  0.00 
C)  0.13 
D)  larger than 1

Question 14

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.

Accepted Answer

a. 0.55
b. 0.8335
c. 0.3465
d.

Question 15

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

Accepted Answer

The answer of Eight individuals are candidates for positions of...

Question 16

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

Accepted Answer

A)  relative method 
B)  probability method 
C)  classical method 
D)  subjective method 
A)  relative method 
B)  probability method 
C)  classical method 
D)  subjective method

Question 17

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.

Accepted Answer

The answer of A small town has 5,600 residents. The...

Question 18

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.

Accepted Answer

The answer of A statistics professor has noted from past...

Question 19

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

Accepted Answer

A)  1/6 
B)  1/36 
C)  1/96 
D)  1/216 
A)  1/6 
B)  1/36 
C)  1/96 
D)  1/216

Question 20

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

Accepted Answer

The answer of How many committees, consisting of 3 female...

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

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

Events that have no sample points in common are

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

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

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

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

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

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

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

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

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

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Comparisons Involving Proportions and a Test of Independence

Simple Linear Regression

Multiple Regression

Filters

Exam 4: Introduction to Probability

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

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

Events that have no sample points in common are

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

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

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

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

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

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

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

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

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

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Comparisons Involving Proportions and a Test of Independence

Simple Linear Regression

Multiple Regression

Filters