Question 1

Which of the following statements is not true regarding probabilities:

Accepted Answer

Probabilities are not merely subjective measures with limited value in business; they are objective assessments used to quantify the likelihood of various outcomes and can significantly inform and improve business decisions.

Question 2

The list of all elementary events for an experiment is called _______.

Accepted Answer

The sample space in probability and statistics is the set of all possible outcomes of an experiment.

Question 3

Which of the following is not a legitimate probability value?

Accepted Answer

Probabilities must be between 0 and 1, inclusive. 5/4 equals 1.25, which is outside this range, making it not a legitimate probability value.

Question 4

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method

Accepted Answer

The classical probability method involves assigning probabilities based on the assumption of equally likely outcomes. In a deck of 52 cards, each card has an equal chance of being drawn, making the probability of drawing the ace of spades 1/52.

Question 5

Given that two events, A and B, are independent, if the marginal probability of A is 0.6, the conditional probability of A given B will be 0.4.

Accepted Answer

If two events, A and B, are independent, the conditional probability of A given B is equal to the marginal probability of A, which is 0.6 in this case, not 0.4.

Question 6

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are mutually exclusive.

Accepted Answer

If the conditional probability of A given B is zero (P(A|B) = 0), it means that event A cannot occur if B has occurred, which is the definition of mutually exclusive events.

Question 7

If P(X|Y)= P(X)then the events are X and Y are independent.

Accepted Answer

If P(X|Y) = P(X), it means the probability of event X occurring given that event Y has occurred is the same as the probability of event X occurring regardless of Y. This implies that the occurrence of Y has no effect on the probability of X occurring, which is the definition of independence between two events.

Question 8

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.The complement of F is ___________.

Accepted Answer

The complement of F, denoted as F', includes all elements in the sample space S that are not in F. Since F = {Betty, Patty, Meagan}, F' = {Albert, Abel, Jack}.

Question 9

In a set of 12 aluminum castings, two castings are defective (D), and the remaining ten are good (G).A quality control inspector randomly selects three of the twelve castings with replacement to test.The sample space for selecting the group to test contains __________ elementary events.

Accepted Answer

The answer of In a set of 12 aluminum castings,...

Question 10

Which of the following is a legitimate probability value?

Accepted Answer

A legitimate probability value must be between 0 and 1, inclusive. 0.28 fits this criterion.

Question 11

If the probability that someone likes the color blue is 44% and the probability that individuals wake up early is 64%, then the probability that individuals who like the color blue and wake up early is about 23%.In this case, the two events are independent.

Accepted Answer

If the two events are independent, the probability of both occurring is the product of their individual probabilities. Thus, the probability of someone liking blue and waking up early would be 0.44 * 0.64 = 0.2816 or 28.16%, not 23%.

Question 12

If X and Y are mutually exclusive events, then if X occurs _______.

Accepted Answer

Mutually exclusive events mean that if one event occurs, the other cannot occur simultaneously.

Question 13

In a set of 25 aluminum castings, four castings are defective (D), and the remaining twenty-one are good (G).A quality control inspector randomly selects three of the twenty-five castings without replacement, to test.The sample space for selecting the group to test contains ____________ elementary events.

Accepted Answer

The answer of In a set of 25 aluminum castings,...

Question 14

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F $\cap$ H is ___________.

Accepted Answer

The intersection of F and H, denoted as F ∩ H, is the set of elements that are common to both F and H. In this case, F = {Betty, Patty, Meagan} and H = {Abel, Meagan}. The only common element between F and H is Meagan, so F ∩ H = {Meagan}.

Question 15

If E and F are mutually exclusive, then _______.

Accepted Answer

Mutually exclusive events cannot happen at the same time, meaning the intersection of E and F (the event that both E and F occur) has a probability of zero.

Question 16

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are independent.

Accepted Answer

If the conditional probability of A given B is zero, it means that if B occurs, A cannot occur, which indicates a dependency between A and B, not independence. Independence would imply that the occurrence of B does not affect the probability of A occurring.

Question 17

Bayes' rule is an extension of the law of conditional probabilities to allow revision of original probabilities with new information.

Accepted Answer

Bayes' rule, indeed, allows for the revision of original probability estimates based on the acquisition of new, relevant information, which is a direct application and extension of the concept of conditional probability.

Question 18

Bayes' rule is a rule to assign probabilities under the relative frequency method.

Accepted Answer

Bayes' rule is a principle in probability theory for updating the probabilities of hypotheses based on observed evidence, not specifically about assigning probabilities under the relative frequency method.

Question 19

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F$\cup$H is ___________.

Accepted Answer

The answer of Consider the following sample space, S, and...

Question 20

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15-years' experience, she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ________________ method.

Accepted Answer

Belinda Bose is using her personal judgment and experience to estimate the probability, which is characteristic of the subjective probability method. This method relies on individual belief or expertise rather than on historical data or predefined models.

Quiz 4: Probability

Which of the following statements is not true regarding probabilities:

The list of all elementary events for an experiment is called _______.

Which of the following is not a legitimate probability value?

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method

Given that two events, A and B, are independent, if the marginal probability of A is 0.6, the conditional probability of A given B will be 0.4.

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are mutually exclusive.

If P(X|Y)= P(X)then the events are X and Y are independent.

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.The complement of F is ___________.

In a set of 12 aluminum castings, two castings are defective (D) , and the remaining ten are good (G) .A quality control inspector randomly selects three of the twelve castings with replacement to test.The sample space for selecting the group to test contains __________ elementary events.

Which of the following is a legitimate probability value?

If the probability that someone likes the color blue is 44% and the probability that individuals wake up early is 64%, then the probability that individuals who like the color blue and wake up early is about 23%.In this case, the two events are independent.

If X and Y are mutually exclusive events, then if X occurs _______.

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F $\cap$ H is ___________.

If E and F are mutually exclusive, then _______.

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are independent.

Bayes' rule is an extension of the law of conditional probabilities to allow revision of original probabilities with new information.

Bayes' rule is a rule to assign probabilities under the relative frequency method.

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F $\cup$ H is ___________.

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15-years' experience, she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ________________ method.

Quiz 4: Probability

Which of the following statements is not true regarding probabilities:

The list of all elementary events for an experiment is called _______.

Which of the following is not a legitimate probability value?

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method

Given that two events, A and B, are independent, if the marginal probability of A is 0.6, the conditional probability of A given B will be 0.4.

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are mutually exclusive.

If P(X|Y)= P(X)then the events are X and Y are independent.

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.The complement of F is ___________.

In a set of 12 aluminum castings, two castings are defective (D) , and the remaining ten are good (G) .A quality control inspector randomly selects three of the twelve castings with replacement to test.The sample space for selecting the group to test contains __________ elementary events.

Which of the following is a legitimate probability value?

If the probability that someone likes the color blue is 44% and the probability that individuals wake up early is 64%, then the probability that individuals who like the color blue and wake up early is about 23%.In this case, the two events are independent.

If X and Y are mutually exclusive events, then if X occurs _______.

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F ∩\cap∩ H is ___________.

If E and F are mutually exclusive, then _______.

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are independent.

Bayes' rule is an extension of the law of conditional probabilities to allow revision of original probabilities with new information.

Bayes' rule is a rule to assign probabilities under the relative frequency method.

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F ∪\cup∪ H is ___________.

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15-years' experience, she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ________________ method.

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F $\cap$ H is ___________.

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F $\cup$ H is ___________.