Question 1

For two events A and B that are not mutually exclusive,the probability that either A or B will occur is P(A)× P(B)- P(A and B).

Accepted Answer

The correct formula for the probability of either A or B occurring is P(A) + P(B) - P(A and B).

Question 2

The use of "expert opinion" is one way to approximate subjective probability values.

Accepted Answer

Expert opinion can provide a useful approximation of subjective probability values in situations where objective data is lacking or incomplete. However, it is important to recognize that expert opinions can be influenced by biases and may not always be accurate.

Question 3

A probability is a numerical statement about the chance that an event will occur.

Accepted Answer

A probability is defined as the measure of the likelihood of an event occurring, typically represented as a number between 0 and 1.

Question 4

Stating that two events are statistically independent means that the probability of one event occurring is independent of the probability of the other event having occurred.

Accepted Answer

This is the definition of statistical independence.

Question 5

Given two statistically independent events (A,B),the joint probability of P(AB)= P(A)+ P(B).

Accepted Answer

The joint probability of two independent events is equal to the product of their individual probabilities, P(AB) = P(A) * P(B). Therefore, the statement P(AB) = P(A) + P(B) is false.

Question 6

Saying that a set of events is mutually exclusive and collectively exhaustive implies that one and only one of the events can occur on any trial.

Accepted Answer

Mutually exclusive events cannot occur at the same time and collectively exhaustive events cover all possible outcomes, so there is only one possible outcome that can occur on any trial.

Question 7

If two events are mutually exclusive,the probability of both events occurring is simply the sum of the individual probabilities.

Accepted Answer

The answer of If two events are mutually exclusive,the probability...

Question 8

Given two statistically independent events (A,B),the conditional probability P(A|B)= P(A).

Accepted Answer

If events A and B are statistically independent, then P(A|B)=P(A)*P(B)/P(B)=P(A). Therefore, the statement is true.

Question 9

A probability density function is a mathematical way of describing Bayes' theorem.

Accepted Answer

A probability density function is a way of describing the likelihood of a continuous random variable taking on a specific value or range of values, while Bayes' theorem is a mathematical principle that relates conditional probabilities of events. While they can be used together in certain applications, they are not the same thing.

Question 10

Bayes' theorem enables us to calculate the probability that one event takes place knowing that a second event has or has not taken place.

Accepted Answer

Bayes' theorem is a formula that allows us to calculate conditional probabilities - the probability of one event given the occurrence of another event. It is useful in fields such as statistics and machine learning.

Question 11

Given two statistically dependent events (A,B),the conditional probability of P(A|B)= P(B)/P(AB).

Accepted Answer

The conditional probability of P(A|B) is equal to P(AB)/P(B), not P(B)/P(AB).

Question 12

If we roll a single die twice,the probability that the sum of the dots showing on the two rolls equals four (4),is 1/6.

Accepted Answer

The probability that the sum of the dots showing on two rolls equals four (4) is 1/36, not 1/6. This can be calculated by listing all the possible outcomes of rolling two dice and finding the number of outcomes that add up to four (4). There are three possible outcomes that add up to four (1+3, 2+2, 3+1) out of 36 possible outcomes (6 possibilities for the first roll and 6 possibilities for the second roll). Therefore, the probability is 3/36, which simplifies to 1/12, not 1/6.

Question 13

Given three statistically independent events (A,B,C),the joint probability of P(ABC)= P(A)× P(B)× P(C).

Accepted Answer

This is true by the definition of independent events. If events A, B, and C are independent, then the probability of all three occurring together is the product of their individual probabilities.

Question 14

A posterior probability is a revised probability.

Accepted Answer

A posterior probability is a revised or updated probability that takes into account new information or evidence.

Question 15

Mutually exclusive events exist if only one of the events can occur on any one trial.

Accepted Answer

Mutually exclusive events cannot occur at the same time, meaning only one event can occur on any one trial.

Question 16

Saying that a set of events is collectively exhaustive implies that one of the events must occur.

Accepted Answer

This is because if a set of events is collectively exhaustive, all possible outcomes must be covered, therefore at least one of the events must occur.

Question 17

Assume that you have a box containing five balls: two red and three white.You draw a ball two times,each time replacing the ball just drawn before drawing the next.The probability of drawing only one white ball is 0.20.

Accepted Answer

The probability of drawing only one white ball in two draws with replacement can be calculated as follows:
P(white on first draw and red on second draw) + P(red on first draw and white on second draw) = (3/5) x (2/5) + (2/5) x (3/5) = 12/25
Therefore, the probability of drawing only one white ball is not 0.20, it is 12/25 or 0.48, which means the statement is false.

Question 18

Subjective probability implies that we can measure the relative frequency of the values of the random variable.

Accepted Answer

Subjective probability does not rely on empirical data, but rather on an individual's personal beliefs or judgments about the likelihood of an event. It is not based on measuring the relative frequency of values of a random variable, which is a characteristic of objective or frequentist probability.

Question 19

Suppose that you enter a drawing by obtaining one of 20 tickets that have been distributed.By using the classical method,you can determine that the probability of your winning the drawing is 0.05.

Accepted Answer

The classical method of probability calculation involves dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there is one favorable outcome (winning the drawing) out of 20 possible outcomes (the 20 distributed tickets). Therefore, the probability of winning is 1/20 = 0.05.

Question 20

The probability,P,of any event or state of nature occurring is greater than or equal to 0 and less than or equal to 1.

Accepted Answer

This is the definition of probability and it is always true. Probability cannot be negative or greater than 1.

Quiz 2: Probability Concepts and Applications