Question 1

If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X | Y) =

Accepted Answer

A) 0.0944 
B) 0.6150 
C) 1.0000 
D) 0.0000 
A) 0.0944 
B) 0.6150 
C) 1.0000 
D) 0.0000 D

Question 2

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

0.9130

Question 3

If P(A) = 0.50, P(B) = 0.40, then, and P(A $\cup$ B) = 0.88, then P(B | A) =

Accepted Answer

A) 0.02 
B) 0.03 
C) 0.04 
D) 0.05 
A) 0.02 
B) 0.03 
C) 0.04 
D) 0.05 C

Question 4

The symbol $\cup$ shows the

Accepted Answer

A) union of events 
B) intersection of two events 
C) sum of the probabilities of events 
D) sample space 
A) union of events 
B) intersection of two events 
C) sum of the probabilities of events 
D) sample space

Question 5

A very short quiz has one multiple choice question with five possible choices (a, b, c, d, e) and one true or false question. Assume you are taking the quiz but do not have any idea what the correct answer is to either question, but you mark an answer anyway.
a.What is the probability that you have given the correct answer to both questions?
b.What is the probability that only one of the two answers is correct?
c.What is the probability that neither answer is correct?
d.What is the probability that only your answer to the multiple choice question is correct?
e.
What is the probability that you have only answered the true or false question correctly?

Accepted Answer

a.1/10
b.5

Question 6

The union of events A and B is the event containing

Accepted Answer

A) all the sample points belonging to B or A 
B) all the sample points belonging to A or B 
C) all the sample points belonging to A or B or both 
D) all the sample points belonging to A or B, but not both 
A) all the sample points belonging to B or A 
B) all the sample points belonging to A or B 
C) all the sample points belonging to A or B or both 
D) all the sample points belonging to A or B, but not both

Question 7

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A $\cup$ B) =

Accepted Answer

A) 0.62 
B) 0.12 
C) 0.60 
D) 0.68 
A) 0.62 
B) 0.12 
C) 0.60 
D) 0.68

Question 8

In statistical experiments, each time the experiment is repeated

Accepted Answer

A) the same outcome must occur 
B) the same outcome can not occur again 
C) a different outcome may occur 
D) a different out come must occur 
A) the same outcome must occur 
B) the same outcome can not occur again 
C) a different outcome may occur 
D) a different out come must occur

Question 9

Assume you have applied for two jobs A and B. The probability that you get an offer for job A is 0.23. The probability of being offered job B is 0.19. The probability of getting at least one of the jobs is 0.38.
a.What is the probability that you will be offered both jobs?
b.Are events A and B mutually exclusive? Why or why not? Explain.

Accepted Answer

a.0.04
b.N

Question 10

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called

Accepted Answer

A) permutation 
B) combination 
C) multiple step experiment 
D) None of these alternatives is correct. 
A) permutation 
B) combination 
C) multiple step experiment 
D) None of these alternatives is correct.

Question 11

If P(A) = 0.50, P(B) = 0.60, and P(A $\cap$ B) = 0.30, then events A and B are

Accepted Answer

A) mutually exclusive events 
B) not independent events 
C) independent events 
D) not enough information is given to answer this question 
A) mutually exclusive events 
B) not independent events 
C) independent events 
D) not enough information is given to answer this question

Question 12

Events A and B are mutually exclusive if their joint probability is

Accepted Answer

A) larger than 1 
B) less than zero 
C) zero 
D) infinity 
A) larger than 1 
B) less than zero 
C) zero 
D) infinity

Question 13

The set of all possible outcomes of an experiment is

Accepted Answer

A) an experiment 
B) an event 
C) the population 
D) the sample space 
A) an experiment 
B) an event 
C) the population 
D) the sample space

Question 14

Assume that in your hand you hold an ordinary six-sided die and a dime. You toss both the die and the dime on a table.
a.What is the probability that a head appears on the dime and a six on the die?
b.What is the probability that a tail appears on the dime and any number more than 3 on the die?
c.What is the probability that a number larger than 2 appears on the die?

Accepted Answer

a.1/12
b.3

Question 15

Events A and B are mutually exclusive. Which of the following statements is also true?

Accepted Answer

A) A and B are also independent. 
B) P(A $\cup$ 
B)  = P(
A) P(
B)  
C) P(A $\cup$ 
B)  = P(
A)  + P(
B)  
D) P(A $\cap$ 
B)  = P(
A)  + P(
B)  
A) A and B are also independent. 
B) P(A $\cup$ 
B)  = P(
A) P(
B)  
C) P(A $\cup$ 
B)  = P(
A)  + P(
B)  
D) P(A $\cap$ 
B)  = P(
A)  + P(
B)

Question 16

If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is

Accepted Answer

A) much larger than any other outcome 
B) much smaller than any other outcome 
C) 1/6 
D) 1/216 
A) much larger than any other outcome 
B) much smaller than any other outcome 
C) 1/6 
D) 1/216

Question 17

The probability assigned to each experimental outcome must be

Accepted Answer

A) any value larger than zero 
B) smaller than zero 
C) at least one 
D) between zero and one 
A) any value larger than zero 
B) smaller than zero 
C) at least one 
D) between zero and one

Question 18

On a recent holiday evening, a sample of 500 drivers was stopped by the police. Three hundred were under 30 years of age. A total of 250 were under the influence of alcohol. Of the drivers under 30 years of age, 200 were under the influence of alcohol.
Let A be the event that a driver is under the influence of alcohol.
Let Y be the event that a driver is less than 30 years old.a. Determine P(A) and P(Y).
b. What is the probability that a driver is under 30 and not under the influence of alcohol?
c. Given that a driver is not under 30, what is the probability that he/she is under the influence of alcohol?
d. What is the probability that a driver is under the influence of alcohol, when we know the driver is under 30?
e. Show the joint probability table.
f. Are A and Y mutually exclusive events? Explain.
g. Are A and Y independent events? Explain.

Accepted Answer

a.P(Y) = 0.6 P(A) =

Question 19

If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A $\cap$ B) =

Accepted Answer

A) 0.76 
B) 1.00 
C) 0.24 
D) 0.20 
A) 0.76 
B) 1.00 
C) 0.24 
D) 0.20

Question 20

In a random sample of UTC students 50% indicated they are business majors, 40% engineering majors, and 10% other majors. Of the business majors, 60% were females; whereas, 30% of engineering majors were females. Finally, 20% of the other majors were female.
a.What percentage of students in this sample was female?
b.Given that a person is female, what is the probability that she is an engineering major?

Accepted Answer

The answer of In a random sample of UTC students...

If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X | Y) =

If P(A) = 0.50, P(B) = 0.40, then, and P(A $\cup$ B) = 0.88, then P(B | A) =

The symbol $\cup$ shows the

The union of events A and B is the event containing

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A $\cup$ B) =

In statistical experiments, each time the experiment is repeated

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called

If P(A) = 0.50, P(B) = 0.60, and P(A $\cap$ B) = 0.30, then events A and B are

Events A and B are mutually exclusive if their joint probability is

The set of all possible outcomes of an experiment is

Events A and B are mutually exclusive. Which of the following statements is also true?

If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is

The probability assigned to each experimental outcome must be

If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A $\cap$ B) =

Data and Statistics

Descriptive Statistics: Tabular and Graphical Presentations

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 X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X | Y) =

If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪\cup∪ B) = 0.88, then P(B | A) =

The symbol ∪\cup∪ shows the

The union of events A and B is the event containing

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A ∪\cup∪ B) =

In statistical experiments, each time the experiment is repeated

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called

If P(A) = 0.50, P(B) = 0.60, and P(A ∩\cap∩ B) = 0.30, then events A and B are

Events A and B are mutually exclusive if their joint probability is

The set of all possible outcomes of an experiment is

Events A and B are mutually exclusive. Which of the following statements is also true?

If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is

The probability assigned to each experimental outcome must be

If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A ∩\cap∩ B) =

Data and Statistics

Descriptive Statistics: Tabular and Graphical Presentations

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

If P(A) = 0.50, P(B) = 0.40, then, and P(A $\cup$ B) = 0.88, then P(B | A) =

The symbol $\cup$ shows the

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A $\cup$ B) =

If P(A) = 0.50, P(B) = 0.60, and P(A $\cap$ B) = 0.30, then events A and B are

If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A $\cap$ B) =