Question 1

Probabilities based on frequency distributions obtained through sampling.&#10;A) objective&#10;B) experimental&#10;C) subjective&#10;D) inexact

Accepted Answer

Frequency distributions obtained through sampling are a type of experimental probability, which is based on actual observation and measurement of events occurring in the real world. A subjective probability is based on an individual's personal beliefs or opinions, while an inexact probability refers to situations where the odds cannot be precisely determined due to lack of information or inherent uncertainty. An objective probability is based on well-defined rules or mathematical principles, but that does not necessarily apply to frequency distributions obtained through sampling.

Question 2

Given evidence E and hypothesis H. The likelihood of sufficiency is computed as&#10;A) the conditional probability of E being true given H is true divided by the conditional probability of E being true given H is false.&#10;B) the conditional probability of E being true given H is true divided by the conditional probability of E being false given H is false.&#10;C) the conditional probability of E being false given H is true divided by the conditional probability of E being true given H is false.&#10;D) the conditional probability of E being false given H is true divided by the conditional probability of E being false given H is false.

Accepted Answer

The likelihood of sufficiency is defined as the ratio of the conditional probability of evidence given the hypothesis is true to the conditional probability of evidence given the hypothesis is false. In other words, it measures how much more likely the evidence is under the hypothesis than under its negation. Therefore, choice A is the correct formula for computing the likelihood of sufficiency.

Question 3

For Bayes theorem to be applied, the following relationship between hypothesis H and evidence E must hold.&#10;A) PH|E) + PH| ~E) = 1&#10;B) PH|E) + P~H| E) = 1&#10;C) PH|E) + PH| ~E) = 0&#10;D) PH|E) + P~H| E) = 0

Accepted Answer

Bayes theorem involves updating a prior probability (PH) based on new evidence (E). Therefore, the sum of the probability of PH given E and the probability of ~H given E (not H) must equal 1. This is because there are only two possibilities, either the hypothesis is true (PH) or it is not (~H). Therefore, the probability of PH given E plus the probability of ~H given E must account for all possible outcomes, which sum up to 1.

Question 4

Computing the probability of picking a heart from a deck of 52 cards can be determined using ______ probability technique.&#10;A) an objective&#10;B) an experimental&#10;C) a subjective&#10;D) an inexact

Accepted Answer

The probability of picking a heart from a deck of 52 cards can be determined using objective probability technique, which is based on theoretical probability determined from counting possible outcomes.

Question 5

This process converts a crisp numeric value to its corresponding degree of membership within a fuzzy set.&#10;A) composition&#10;B) inference&#10;C) fuzzification&#10;D) defuzzification

Accepted Answer

Fuzzification is the process of converting a crisp (exact) numerical value into its equivalent fuzzy set membership value. It involves mapping a numerical input to a membership value within a given fuzzy set.

Question 6

The probability that a person owns a sports car given that they subscribe to at least one automotive magazine is 40%. We also know that 3% of the adult population subscribes to at least one automotive magazine. Finally, the probability of a person owning a sports car given that they don't subscribe to at least one automotive magazine is 30%. Use this information together with Bayes theorem to compute the probability that a person subscribes to at least one automotive magazine given that they own a sports car.
Answers to Chapter 13 Questions
Multiple Choice Questions

Accepted Answer

The answer of The probability that a person owns a...

Question 7

This technique is used to determine the height of a rule consequent membership function as determined by the truth of the rule's antecedent condition.&#10;A) fuzzy set union&#10;B) fuzzy set intersection&#10;C) center of gravity&#10;D) clipping

Accepted Answer

Clipping is the technique used to determine the height of a rule consequent membership function based on the truth of the rule's antecedent condition. This involves "clipping" the consequent membership function at a height corresponding to the degree of truth of the antecedent.

Question 8

With Bayes theorem the probability of hypothesis H- specified by PH) - is referred to as&#10;A) an a priori probability&#10;B) a conditional probability&#10;C) a posterior probability&#10;D) a bidirectional probability

Accepted Answer

An a priori probability is the initial probability of a hypothesis before any evidence is taken into account, as specified by Bayes' theorem.

Question 9

A fuzzy set is associated with a&#10;A) linguistic variable.&#10;B) certainty factor.&#10;C) hypothesis to be tested.&#10;D) linguistic value.

Accepted Answer

The answer of A fuzzy set is associated with a&#10;A)...

Question 10

A car mechanic tells you that there is a 75% chance that your car will need major repair work within the next six months. This statement is an example of&#10;A) an objective probability.&#10;B) an experimental probability.&#10;C) a subjective probability.&#10;D) a fuzzy probability.

Accepted Answer

This statement is based on the mechanic's personal opinion, knowledge, and experience with cars, rather than being a calculated probability based on data or experiments. Therefore, it is a subjective probability.

Deck 13: Managing Uncertainty in Rule-Based Systems