Question 1

The probability of a student attending every college class is p = .26.The probability of a student attending every college class and earning an A is p = .22.Hence,the probability of a student earning an A,given that he or she attends every college class,is
A)p = .06
B)p = .48
C)p = .85
D)There is not enough information to answer this question.

Accepted Answer

We can use the formula for conditional probability, which is P(A|B) = P(A and B) / P(B). In this case, A is the student earning an A and B is the student attending every college class. We are given that P(B) = 0.26 and P(A and B) = 0.22. Therefore, P(A|B) = 0.22 / 0.26 = 0.85. So the probability of a student earning an A, given that he or she attends every college class, is 0.85.

Question 2

A researcher records the number of job openings among small businesses.She finds that the probability that a small business has 0 job openings is p = .22;1 job opening is p = .45;2 job openings is p = .08;and 3 job openings is p = .25.What is the probability that a small business has at least 2 job openings?
A).08
B).25
C).33
D).67

Accepted Answer

The probability of a small business having at least 2 job openings is equal to the sum of the probability of having 2 job openings plus the probability of having 3 job openings.

P(2 or more job openings) = P(2 job openings) + P(3 job openings) 
= .08 + .25 
= .33

Therefore, the best choice is C) .33.

Question 3

When the sum of the probabilities of two outcomes is exhaustive of all possible outcomes,these outcomes are referred to as
A)mutually exclusive
B)complementary
C)independent
D)conditional

Accepted Answer

When the sum of the probabilities of two outcomes is exhaustive of all possible outcomes, these outcomes are referred to as complementary. This means that the two outcomes are the only possible outcomes and they cannot happen at the same time. For example, in a coin toss, the only possible outcomes are heads or tails and they are complementary since the probability of getting heads added to the probability of getting tails is equal to 1.

Question 4

The probability of a team having a sellout crowd is p = .45.The probability of having a sellout crowd and the team winning is p = .32.Hence,the probability of a team winning,given that they have a sellout crowd,is
A)p = .71
B)p = .77
C)p = .14
D)There is not enough information to answer this question.

Accepted Answer

The probability of the team winning given a sellout crowd is calculated using the formula for conditional probability: P(A|B) = P(A and B) / P(B). Here, P(A and B) = .32 (probability of sellout and win), and P(B) = .45 (probability of sellout). Thus, P(A|B) = .32/.45 = .71.

Question 5

Suppose you open a new game at the county fair.When patrons win,you pay them $3.00;when patrons lose,they pay you $1.00.If the probability of a patron winning is p = .20,then how much can you expect to win (or lose)in the long run? Hint: You need to compute the expected value of the mean.
A)win 0.20 cents per play
B)win 0.60 cents per play
C)lose 0.80 cents per play
D)lose 2.20 dollars per play

Accepted Answer

The answer of Suppose you open a new game at...

Question 6

A professor records the grades for his class of students.He finds that the probability that a student earns an A is p = .14;earns a B is p = .36;earns a C is p = .32;earns a D is p = .10;and earns an F is p = .08.What is the probability that a student earns a B or better in this class?
A).36
B).14
C).86
D).50

Accepted Answer

The answer of A professor records the grades for his...

Question 7

Which of the following is a mathematical formula that relates the conditional and marginal (unconditional)probabilities of two conditional outcomes that occur at random?
A)Bayes' theorem
B)simple probability
C)random event sampling
D)descriptive statistics

Accepted Answer

Bayes' theorem is a formula that relates the conditional and marginal (unconditional) probabilities of two conditional outcomes that occur at random. It is widely used in fields such as statistics, computer science, engineering, and genetics. Option B (simple probability) is too general and does not specifically relate to conditional and marginal probabilities. Option C (random event sampling) and Option D (descriptive statistics) do not involve the relationship between conditional and marginal probabilities.

Question 8

Which rule states that when two outcomes are independent,the probability that these outcomes occur together is the product of their individual probabilities?
A)additive rule
B)multiplicative rule
C)both A and B
D)none the of above

Accepted Answer

The Multiplicative Rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities. This rule is widely used in probability calculations and is important in many fields, including statistics, engineering, and finance. The Additive Rule, on the other hand, applies when events are mutually exclusive, and states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. Therefore, the correct answer is B.

Question 9

Bayes' theorem is often applied to a variety of ________ probability situations,including those related to statistical inference.
A)generic
B)absolute
C)conditional
D)fixed

Accepted Answer

Bayes' theorem is specifically designed to deal with conditional probabilities, where the occurrence of one event is dependent on the occurrence of another event. It is commonly used in statistical inference to update prior probabilities based on observed data.

Question 10

The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a
A)random variable
B)probability distribution
C)conditional probability
D)sample space

Accepted Answer

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take. The sum of probabilities for each outcome must equal to 1.00. Random variable refers to the variable itself, while conditional probability refers to the likelihood of an event occurring given that another event has occurred. Sample space is the set of all possible outcomes of a random experiment.

Question 11

Suppose that the probability that any child of alcoholic parents becomes alcoholic is p = .16.Assuming independent outcomes,the probability that two children of alcoholic parents will be alcoholic equals
A).16
B).32
C).25
D).03

Accepted Answer

The probability that two independent events both happen is the product of their individual probabilities. So, the probability that both children will be alcoholic is $0.16 \times 0.16 = 0.0256$, which rounds to $0.03$.

Question 12

Below is the probability distribution for random variable x.What is the probability of at least a score of 2 in this distribution? 
A).18
B).42
C).60
D).82

Accepted Answer

To calculate the probability of at least a score of 2, we need to add the probabilities for x = 2, x = 3, and x = 4, because these are the only outcomes that have a score of 2 or higher.

P(at least 2) = P(X = 2) + P(X = 3) + P(X = 4) 
              = 0.20 + 0.35 + 0.27 
              = 0.82

Therefore, the probability of at least a score of 2 in this distribution is 0.82, which corresponds to option D).

Question 13

When the probability of one outcome changes depending on the occurrence of a second outcome,these outcomes are referred to as
A)mutually exclusive
B)complementary
C)independent
D)conditional

Accepted Answer

When the probability of one outcome changes depending on the occurrence of a second outcome, it is referred to as a conditional probability. This means that the occurrence of the first outcome is dependent on the occurrence of the second. Conditions probabilities are not mutually exclusive or complementary, and may or may not be independent depending on the specific scenario.

Question 14

Below is the probability distribution for random variable x.Which of the following is most probable? 
A)a score of at most 13
B)a score of at least 13
C)a score of 12
D)a score of 14

Accepted Answer

The probability of getting a score of at most 13 is the sum of the probabilities of getting a score of 12 or 13, which is 0.2 + 0.4 = 0.6. This is the highest probability among the given choices.

Question 15

The probability of a college student being employed is p = .35.The probability of a student being employed and dropping out of college is p = .20.Hence,the probability of a student dropping out of college,given that he or she is employed,is
A)p = .07
B)p = .57
C)p = .55
D)There is not enough information to answer this question.

Accepted Answer

We can use Bayes' theorem to solve this problem:

P(dropping out | employed) = P(employed | dropping out) * P(dropping out) / P(employed)

We know that P(employed | dropping out) = 0.20 (from the given information) and P(dropping out) = unknown.

To find P(employed), we can use the Law of Total Probability:

P(employed) = P(employed | dropping out) * P(dropping out) + P(employed | not dropping out) * P(not dropping out)

From the information given, we don't know P(not dropping out), so we can't solve for P(employed) exactly. However, we can make a reasonable assumption that P(not dropping out) is greater than P(dropping out), since dropping out is a less likely event. Therefore, we can estimate P(employed) as:

P(employed) ≈ P(employed | dropping out) * P(dropping out)

Now we can plug in our values:

P(dropping out | employed) = 0.20 * P(dropping out) / (0.35)

Simplifying,

P(dropping out | employed) = 0.57 * P(dropping out)

Since the probability of dropping out cannot be negative or greater than 1, we know that P(dropping out) must be between 0 and 1/0.57 ≈ 1.75. This is a very wide range, but the only answer choice that falls within it is B, p = 0.57. Therefore, B is the best choice.

Question 16

A researcher records the number of mistakes made during a memory skills task.He finds that the probability that participants in this study made 0 mistakes is p = .22;made 1 mistake is p = .30;made 2 mistakes is p = .16;made 3 mistakes is p = .12;and made 4 or more mistakes is p = .25.Is this probability distribution accurate?
A)Yes,it distributes all possible outcomes for the random variable.
B)No,one of the outcomes is stated as "or more."
C)No,the probability distribution does not sum to 1.0.
D)both B and C

Accepted Answer

The answer of A researcher records the number of mistakes...

Question 17

Below is the probability distribution for the number of times students had to take the same exam before passing it.If a student must pass the exam in two tries of less to pass the class,then what is the probability of passing the class? 
A).80
B).40
C).20
D).10

Accepted Answer

The probability distribution shows that there is a .8 probability of passing the exam in two tries or less. Since a student must pass in two tries or less to pass the class, the probability of passing the class is .8 or 80%. Therefore, the best choice is A).

Question 18

The probability that a parent rewards a child with a dessert for eating a healthy meal is .07.Assuming independent outcomes,the probability that two parents reward their child's healthy eating equals
A).07
B).14
C).05
D).005

Accepted Answer

Since the events are independent, we can use the multiplication rule for independent events to find the probability of both parents rewarding their child.

P(both parents reward) = P(first parent rewards) * P(second parent rewards)

= .07 * .07

= .0049

≈ .005

Therefore, the probability that two parents reward their child's healthy eating is 0.005 or choice D.

Question 19

Which of the following probability distributions is accurate?
A)45/80,20/80,20/80,10/80
B)10/80,23/80,37/80,10/80
C)ñ20/80,40/80,40/80,20/80
D)none of the above

Accepted Answer

The probabilities in option B add up to 1, which is a requirement for a valid probability distribution.

Question 20

The mean of a probability distribution is called the
A)expected value of the mean
B)mathematical expectation
C)both A and B
D)none of the above

Accepted Answer

The answer of The mean of a probability distribution is...

Quiz 5: Probability, Normal Distributions, and Z Scores

The probability of a student attending every college class is p = .26.The probability of a student attending every college class and earning an A is p = .22.Hence,the probability of a student earning an A,given that he or she attends every college class,is

When the sum of the probabilities of two outcomes is exhaustive of all possible outcomes,these outcomes are referred to as

The probability of a team having a sellout crowd is p = .45.The probability of having a sellout crowd and the team winning is p = .32.Hence,the probability of a team winning,given that they have a sellout crowd,is

Suppose you open a new game at the county fair.When patrons win,you pay them $3.00;when patrons lose,they pay you $1.00.If the probability of a patron winning is p = .20,then how much can you expect to win (or lose) in the long run? Hint: You need to compute the expected value of the mean.

A professor records the grades for his class of students.He finds that the probability that a student earns an A is p = .14;earns a B is p = .36;earns a C is p = .32;earns a D is p = .10;and earns an F is p = .08.What is the probability that a student earns a B or better in this class?

Which of the following is a mathematical formula that relates the conditional and marginal (unconditional) probabilities of two conditional outcomes that occur at random?

Which rule states that when two outcomes are independent,the probability that these outcomes occur together is the product of their individual probabilities?

Bayes' theorem is often applied to a variety of ________ probability situations,including those related to statistical inference.

The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a

Suppose that the probability that any child of alcoholic parents becomes alcoholic is p = .16.Assuming independent outcomes,the probability that two children of alcoholic parents will be alcoholic equals

Below is the probability distribution for random variable x.What is the probability of at least a score of 2 in this distribution?

When the probability of one outcome changes depending on the occurrence of a second outcome,these outcomes are referred to as

Below is the probability distribution for random variable x.Which of the following is most probable?

The probability of a college student being employed is p = .35.The probability of a student being employed and dropping out of college is p = .20.Hence,the probability of a student dropping out of college,given that he or she is employed,is

Below is the probability distribution for the number of times students had to take the same exam before passing it.If a student must pass the exam in two tries of less to pass the class,then what is the probability of passing the class?

The probability that a parent rewards a child with a dessert for eating a healthy meal is .07.Assuming independent outcomes,the probability that two parents reward their child's healthy eating equals

Which of the following probability distributions is accurate?

The mean of a probability distribution is called the