Question 1

The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of its occurrence.

Accepted Answer

This is the correct definition of the complement rule in probability theory.

Question 2

The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events.

Accepted Answer

Rolling a 3 and rolling a 2 are mutually exclusive events because they cannot happen at the same time with a single roll of a die.

Question 3

The probability of rolling a 3 or 2 on a single die is an example of conditional probability.

Accepted Answer

Conditional probability involves the probability of an event occurring given that another event has already occurred. Rolling a 3 or 2 on a single die is an example of basic probability, where the probability of each event is independent and not conditioned on any other event.

Question 4

If two events A and B are mutually exclusive, what does the special rule of addition state?

Accepted Answer

The special rule of addition states that if two events A and B are mutually exclusive, then the probability of either A or B occurring is equal to the sum of the probabilities of A and B individually, hence option A is the correct choice. Option B is incorrect as mutually exclusive events cannot occur together. Option C is incorrect as it combines probabilities for both "and" and "or" events. Option D is incorrect as it results in a negative probability, which is not possible.

Question 5

A combination of a set of objects is defined by the order of the objects.

Accepted Answer

A combination only considers the selection of objects, not the order in which they are chosen. The order of selection does not matter in a combination.

Question 6

If two events are mutually exclusive,then P(A and
B)= P(A)× P(B).

Accepted Answer

If two events are mutually exclusive, it means that they cannot occur at the same time. Therefore, the probability of both events occurring together is zero, and the formula P(A and B) = P(A) × P(B) is not applicable. The correct formula for mutually exclusive events is P(A or B) = P(A) + P(B).

Question 7

An illustration of an experiment is turning the ignition key of an automobile as it comes off the assembly line to determine whether or not the engine will start.

Accepted Answer

This is an example of an experiment as it involves manipulating a variable (turning the ignition key) to observe the outcome (whether or not the engine starts).

Question 8

Bayes' theorem is used to calculate a subjective probability.

Accepted Answer

Bayes' theorem is used to calculate a conditional probability, not a subjective probability.

Question 9

If there are "m" ways of doing one thing,and "n" ways of doing another thing,the multiplication formula states that there are (m)× (n)ways of doing both.

Accepted Answer

This is the statement of the multiplication principle in combinatorics. It states that if there are m ways to do one task and n ways to do another task, then there are m x n ways to do both tasks together. This principle is applicable in many real-world scenarios, such as counting the number of possible outcomes of a sequence of events.

Question 10

What does the complement rule state?

Accepted Answer

The complement rule states that the probability of an event A occurring is equal to 1 minus the probability of A not occurring. This is mathematically represented as P(A) = 1 – P(not A). Choice B correctly represents this rule. Choice A looks like a variation of the subtraction rule. Choice C looks like the multiplication rule. Choice D does not represent any statistical rule.

Question 11

An individual can assign a subjective probability to an event based on the individual's knowledge about the event.

Accepted Answer

Subjective probability is based on an individual's personal judgment and experiences, and it can be influenced by their knowledge, beliefs, and biases. Therefore, an individual can assign a subjective probability to an event based on their knowledge about it.

Question 12

Bayes' theorem is a method to revise the probability of an event given additional information.

Accepted Answer

Bayes' theorem is a fundamental concept in probability theory used to update the probability of an independent event, given new information or evidence. It is also known as Bayes' rule or Bayes' law.

Question 13

A study of 200 computer service firms revealed these incomes after taxes:  What is the probability that a particular firm selected has $1 million or more in income after taxes?

Accepted Answer

The answer of A study of 200 computer service firms...

Question 14

The joint probability of two independent events,A and B,is computed as P(A and
B)= P(A)× P(B).

Accepted Answer

The statement is true. When two events are independent, the probability of both events occurring together is the product of their individual probabilities.

Question 15

The joint probability of two events,A and B,that are NOT independent is computed as
P(A and
B)= P(A)× P(B|A).

Accepted Answer

This is the formula for the joint probability of two events that are not independent.

Question 16

A coin is tossed four times. The joint probability that all four tosses will result in a head is 1/4 or 0.25.

Accepted Answer

The joint probability of all four tosses resulting in a head is (1/2)^4 = 1/16 or 0.0625, which is not equal to 0.25. Therefore, the statement is false.

Question 17

The National Center for Health Statistics reported that of every 883 deaths in recent years,24 resulted from an automobile accident,182 from cancer,and 333 from heart disease. What is the probability that a particular death is due to an automobile accident?

Accepted Answer

The probability of a particular death being due to an automobile accident can be calculated by dividing the number of deaths due to automobile accidents by the total number of deaths, which is 883. Thus, the probability is 24/883 or 0.027.

Question 18

A joint probability measures the likelihood that two or more events will happen concurrently.

Accepted Answer

This is the definition of a joint probability.

Question 19

To apply the special rule of addition,the events must be mutually exclusive.

Accepted Answer

For the special rule of addition to apply, the events must be mutually exclusive, meaning they cannot occur at the same time. This ensures that the probability of either event occurring is the sum of their individual probabilities.

Question 20

Which approach to probability is exemplified by the following formula? Probability of an event =

Accepted Answer

The answer of Which approach to probability is exemplified by...

Quiz 5: A Survey of Probability Concepts