Question 1

If A and B are mutually exclusive events, then A  B can never occur on the same trial of an experiment.

Accepted Answer

By definition, mutually exclusive events cannot occur at the same time. Therefore, A and B cannot occur on the same trial of an experiment if they are mutually exclusive.

Question 2

A table, graph, or formula that associates each possible value of a discrete random variable, x, with its probability of occurrence, p(x), is called a discrete probability distribution.

Accepted Answer

This is the correct definition of a discrete probability distribution.

Question 3

The additive rule of probability is used to compute the probability of an intersection of two or more events. In other words, given two events A and B,  and also

Accepted Answer

The answer of The additive rule of probability is used...

Question 4

If A and B are dependent events, they are also mutually exclusive.

Accepted Answer

If events A and B are dependent, it means that the occurrence of one affects the probability of the occurrence of the other. On the other hand, if events A and B are mutually exclusive, it means that the occurrence of one event excludes the occurrence of the other. Therefore, dependent events cannot be mutually exclusive.

Question 5

All the outcomes contained in one or the other of two events (or possibly in both) constitute the union of two events.

Accepted Answer

This is the definition of the union of two events in probability theory.

Question 6

If x is a discrete random variable, then x can take on only one of two possible values.

Accepted Answer

A discrete random variable can take on more than two possible values, as long as those values are countable integers or whole numbers.

Question 7

A random variable is any variable for which the numerical value is determined by a random experiment, and, thus, by chance.

Accepted Answer

A random variable is exactly that - a variable whose value is determined by chance or randomness.

Question 8

A set of all possible values of a discrete random variable is countable, because the variable can assume values only at specific points on a scale of values, with inevitable gaps in between.

Accepted Answer

A discrete random variable can only take on a finite or countably infinite set of values. Therefore, the set of all possible values is also countable. This is because the values are specific points on a scale, and there are only a finite or countable number of these points, with gaps in between.

Question 9

A false negative in screening tests is the event that the test is positive for a given condition, given that the person does not have the condition.

Accepted Answer

A false negative in screening tests is the event that the test is negative for a given condition, given that the person actually has the condition.

Question 10

Given a set of events  that are mutually exclusive and exhaustive and an event A, the law of total probability states that P(A) can be expressed as

Accepted Answer

The law of total probability states that when we have a set of events that are mutually exclusive and exhaustive, the probability of an event A occurring can be expressed as the sum of the probabilities of A occurring given each of the possible outcomes in the set.

Question 11

There are two types of random variables: discrete and continuous.

Accepted Answer

This statement is true. Random variables can be classified as either discrete, where the variable takes on a finite or countably infinite set of possible values, or continuous, where the variable can take on any value within a certain range or interval.

Question 12

The time required to assemble a computer could be classified as a discrete random variable.

Accepted Answer

The time required to assemble a computer is a continuous random variable because it can take any value within a range, not just distinct, separate values.

Question 13

Bayes' Rule is a formula for revising an initial subjective (prior) probability value on the basis of results obtained by an empirical investigation, thereby obtaining a new (posterior) probability value.

Accepted Answer

This is the definition of Bayes' Rule.

Question 14

If A and B are independent events, they are also mutually exclusive.

Accepted Answer

Independent events can occur simultaneously, while mutually exclusive events cannot occur together. Therefore, if events A and B are independent, they can still occur at the same time and are not mutually exclusive.

Question 15

The addition law of probability theory is used to compute the probability for the occurrence of a union of two or more events; namely, given two events A and B,

Accepted Answer

This is the definition of the addition law of probability.

Question 16

A false positive in screening tests is the event that the test is negative for a given condition, given that the person has the condition.

Accepted Answer

A false positive in screening tests is the event that the test is positive for a given condition, given that the person does not have the condition.

Question 17

The probability distribution for a discrete variable x is a formula, a table, or a graph providing or showing p(x), the probability associated with each of the values of x.

Accepted Answer

This statement is true. The probability distribution for a discrete variable x does indeed show the probability associated with each of the possible values of x. This can be presented in the form of a formula, a table or a graph.

Question 18

If P(A/B) = P(A  B), then A and B are independent events.

Accepted Answer

The answer of If P(A/B) = P(A  B), then...

Question 19

The number of students living off-campus is an example of a discrete random variable.

Accepted Answer

The number of students living off-campus can only take on certain, distinct values (such as 0, 1, 2, etc.) and is not continuous, making it a discrete random variable.

Question 20

Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A  B) = 0.2. Then P(B/A) = 0.4.

Accepted Answer

P(B/A) = P(A 11eab386_b975_8e32_aec0_f9ce24f03c0d_TB4962_11 B) / P(A) = 0.2 / 0.4 = 0.5, which is not equal to 0.4. Therefore, the statement is false.

Quiz 4: A: probability and Probability Distributions

If A and B are mutually exclusive events, then A B can never occur on the same trial of an experiment.