Question 1

Two events are independent if ________.

Accepted Answer

If two events are independent, the probability of one event occurring does not affect the probability of the other event occurring. In other words, the probability of each event is not affected by the other. Therefore, choice B is the best answer.

Question 2

There are four mammals (one dog and three cats)and three reptiles (one snake and two turtles)on sale at a drastic discount at the local pet store.What is the probability that the first two animals sold are both cats?

Accepted Answer

The answer of There are four mammals (one dog and...

Question 3

What is the probability of flipping a quarter three times and getting tails all three times?

Accepted Answer

The answer of What is the probability of flipping a...

Question 4

Given the probability of event G is  ,the probability of event H is  ,the probability of both events G and H is  =  .This is an example of the two events being ________.

Accepted Answer

The answer of Given the probability of event G is...

Question 5

A continuous random variable is ________.

Accepted Answer

A continuous random variable can take on any value within one or more intervals of real numbers, and there are an infinite number of possible values. It cannot be counted like a discrete random variable (Choice A). A probability distribution (Choice C) describes the possible values and their associated probabilities, but does not define the variable itself. A variable with only one possible value (Choice D) is a deterministic variable and not a random variable.

Question 6

The likelihood that an individual prefers a Ford Mustang convertible is based on the proportion of the population that prefers a Ford Mustang that also prefers a convertible.This is an example of ________.

Accepted Answer

The situation described involves the probability of one event (preference for a Mustang) occurring given that another event (preference for a convertible) has already occurred. This is an example of conditional probability.

Question 7

Which of the following is true of random variables?

Accepted Answer

Random variables may not have a physical or natural meaning.

Question 8

Conditional probability is the probability of ________.

Accepted Answer

Conditional probability deals with the probability of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the intersection of the two events by the probability of the given condition event.

Question 9

A discrete random variable is ________.

Accepted Answer

A discrete random variable is a variable that has a countable number of values, meaning that the number of possible outcomes can be counted. Option A describes a continuous random variable, option B describes the probability distribution of a random variable, and option D describes a constant random variable.

Question 10

For a discrete random variable A,the probability distribution of the discrete outcomes is called a ________.

Accepted Answer

The probability distribution of a discrete random variable A is called the probability mass function, denoted by f(a). This function assigns a probability to each possible value of A, such that the sum of probabilities over all possible values of A equals 1. Therefore, the best choice is C. The other options are either not applicable to probability distributions or do not accurately describe the probability distribution of a discrete random variable.

Question 11

A random variable is a function that assigns a real number to ________.

Accepted Answer

A random variable is a function that maps each outcome in a given sample space to a real number. Therefore, option B is the correct choice as it correctly describes the assignment of a real number to each outcome in a sample space. Option A is incorrect as a random variable does not necessarily assign a real number to each event in a sample space, but only to each outcome. Option C is incorrect as a sample space is a collection of all possible outcomes for an experiment, and not an experiment itself. Option D is also incorrect as a random variable does not assign a real number to a sample space, but rather to each outcome within the sample space.

Question 12

All of the following are continuous random variables except ________.

Accepted Answer

The number of tires is a discrete variable because it can only take on certain specific values (such as 2, 4, or 6), rather than being able to take on any value within a range. The other options are all continuous variables because they can take on any value within a certain range (e.g. the Dow Jones could go up or down by any amount, the height of a person could be any value in inches, and the temperature could be any value in degrees Fahrenheit).

Question 13

All of the following are examples of discrete random variables except ________.

Accepted Answer

The income of an American family is a continuous random variable, as it can take on any numerical value within a specified range. The other options are discrete random variables, as they can only take on a finite or countable number of values.

Question 14

Consider the following table that shows the details of the people applying for a particular job.The cell numbers indicate the number of applicants belonging to a particular age group and gender.  What is the probability that a female or someone less than 41 years old is chosen?

Accepted Answer

The answer of Consider the following table that shows the...

Question 15

At the Simple Sub Shop,there are five types of sandwiches and three different beverages.Lunch Special A consists of a club sandwich and a cola.What is the probability that someone would choose a sandwich and a beverage at random and end up with Lunch Special A?

Accepted Answer

The answer of At the Simple Sub Shop,there are five...

Question 16

In an experiment,a random variable is ________.

Accepted Answer

A random variable is a numerical description of the outcome of an experiment. It represents a value that is determined by chance and can take on different values based on the outcome of the experiment. It is not necessarily picked from a set of values that all have an equal chance of occurring or chosen at random from a distribution list. It also cannot be an outcome that has zero chances of occurring.

Question 17

Which of the following cannot be used to develop a probability distribution?

Accepted Answer

Stating that there is a definite chance of rain tomorrow does not provide any quantitative data that can be used to develop a probability distribution. The other options involve collecting data that can be used to determine the probability of certain outcomes.

Question 18

Two events are mutually exclusive as long as ________.

Accepted Answer

Mutually exclusive events have no outcomes in common.

Question 19

Five identical boxes are kept with different amounts of money in them.It is known that they contain $5,$10,$15,$20,and $50,although it is not clear which box contains what amount of money.What is the chance of choosing a box that contains either an amount greater than $10 or an amount that is evenly divisible by ten?

Accepted Answer

The answer of Five identical boxes are kept with different...

Question 20

The law of probability that is used to calculate conditional probability is called ________.

Accepted Answer

The law of probability that is used to calculate conditional probability is called the multiplication law. It states that the probability of A and B occurring together is equal to the probability of A multiplied by the probability of B given A. It is used to calculate the probability of two events occurring together when the occurrence of one event affects the probability of the other event.

Quiz 3: Probability Concepts and Distributions