Question 1

Events that have no sample space outcomes in common,and,therefore cannot occur simultaneously are referred to as independent events.

Accepted Answer

This is a definition of mutually exclusive events.

Question 2

A contingency table is a tabular summary of probabilities concerning two sets of complementary events.

Accepted Answer

A contingency table displays the frequency or proportion of observations that fall into each category of two or more categorical variables for complementary events. This table can be used to calculate probabilities of different outcomes or events.

Question 3

If events A and B are independent,then P(A|B)is always equal to zero.

Accepted Answer

If events A and B are independent, then P(A|B) = P(A), which is not necessarily equal to zero. In fact, if P(A) is nonzero, then P(A|B) will also be nonzero.

Question 4

Mutually exclusive events have a nonempty intersection.

Accepted Answer

Mutually exclusive events have no intersection, meaning they are completely separate from one another.

Question 5

Events that have no sample space outcomes in common,and therefore,cannot occur simultaneously are:

Accepted Answer

Mutually exclusive events are those that have no sample space outcomes in common and therefore cannot occur simultaneously. This means that if one event occurs, the other event cannot occur at the same time.

Question 6

An event is a collection of sample space outcomes.

Accepted Answer

An event is defined as a subset of the sample space, which means it is a collection of sample space outcomes. Therefore, the statement is true.

Question 7

A ____________ is the probability that one event will occur given that we know that another event already has occurred.

Accepted Answer

The definition matches exactly with the concept of conditional probability, where the probability of an event A given that event B has occurred is denoted as P(A|B). The expression captures the fact that the information about the occurrence of B has narrowed down the sample space, and the calculation of the probability of A should take this into account. Option A refers to a potential outcome in the sample space, but it is not related to the question. Option B refers to subjective beliefs, which are not necessarily based on any previous events. Option C refers to the complement of an event, which is the probability of its non-occurrence, and does not depend on the occurrence of another event. Option D refers to the concept of relative frequency, but it does not take into account any conditioning information.

Question 8

If events A and B are mutually exclusive,then P(A  B)is always equal to zero.

Accepted Answer

If events A and B are mutually exclusive, it means they cannot occur together. Therefore, the probability of both events happening at the same time is zero.

Question 9

A subjective probability is a probability assessment that is based on experience,intuitive judgment,or expertise.

Accepted Answer

A subjective probability is based on subjective factors such as experience, intuition, or expertise, and may not be based on mathematical or statistical principles.

Question 10

If P(A)> 0 and P(B)> 0 and events A and B are independent,then:

Accepted Answer

B)= P(A)P(B A)

Question 11

The set of all possible experimental outcomes is called a(n):

Accepted Answer

The sample space is the set of all possible outcomes that can occur in an experiment. It includes both the favorable and unfavorable outcomes. Therefore, option A is the correct choice. Option B refers to a subset of the sample space, option C refers to the entire experiment or process, and option D refers to the likelihood or chance of a particular outcome occurring.

Question 12

If events A and B are independent,then the probability of simultaneous occurrence of event A and event B can be found with:

Accepted Answer

All of the above are correct because the probability of simultaneous occurrence of event A and event B can be found with P(A)P(B), P(A)P(A|B), or P(B)P(A|B).

Question 13

The _______ of two events X and Y is another event that consists of the sample space outcomes belonging to either event X or event Y or both event X and Y.

Accepted Answer

The definition provided in the question corresponds to the union of two events. The complement of an event consists of all sample space outcomes that do not belong to the event. Intersection refers to the set of sample space outcomes that belong to both events X and Y. Conditional probability refers to the probability of one event occurring given that another event has occurred. Therefore, the best choice for the blank is option B, which is the union of two events.

Question 14

___________________ is a measure of the chance that an uncertain event will occur.

Accepted Answer

Probability is defined as the measure of the likelihood of an event occurring. It is a numerical value between 0 and 1 (inclusive) representing the chance of an event occurring.

Question 15

The probability of an event is the sum of the probabilities of the sample space outcomes that correspond to the event.

Accepted Answer

This statement is a correct definition of probability.

Question 16

A manager has just received the expense checks for six of her employees.She randomly distributes the checks to the six employees.What is the probability that exactly five of them will receive the correct checks (checks with the correct names)?

Accepted Answer

If exactly 5 employees get the correct checks, then the remaining employee must also receive the correct check. Since the manager randomly distributes the checks, the probability of any one employee receiving the correct check is 1/6. Therefore, the probability of all six employees receiving the correct check is (1/6)^6, which is a very small probability. Since the remaining employee must also receive the correct check in order for exactly 5 employees to get the correct check, the probability is 0. Therefore, the best choice is D.

Question 17

If two events are independent,we can _____ their probabilities to determine the intersection probability.

Accepted Answer

If two events are independent, their probabilities can be multiplied to determine the probability of both events occurring together. This is known as the intersection probability, or the probability of the intersection of the two events.

Question 18

If events A and B are mutually exclusive,then P(A|B)is always equal to zero.

Accepted Answer

If events A and B are mutually exclusive, it means that they cannot occur at the same time. Therefore, the probability of A given that B has occurred is zero, because if B has occurred, A cannot occur.

Question 19

Two mutually exclusive events having positive probabilities are ______________ dependent.

Accepted Answer

The answer of Two mutually exclusive events having positive probabilities...

Question 20

Two events are independent if the probability of one event is influenced by whether or not the other event occurs.

Accepted Answer

Two events are independent if the occurrence of one event does not affect the probability of the other event. Therefore, the statement in the question is reversed and incorrect.

Quiz 4: Probability