Question 1

The likelihood of observing each of two events is referred to as a:
A)hypothesis
B)binomial probability
C)conditional probability
D)joint probability

Accepted Answer

The joint probability refers to the probability of observing both events together. Therefore, it is the appropriate choice as it describes the likelihood of observing each of two events.

Question 2

Let event A be "satisfied with one's marriage" and event B be "satisfied with one's job.The probability that someone is satisfied with both his marriage and his job is equal to:
A)p(A|B)
B)p(A,B)
C)p(B)p(A|B)
D)b and c

Accepted Answer

The probability that someone is satisfied with both their marriage and job can be calculated using the conditional probability formula:

P(A and B) = P(A | B) * P(B)

This formula can be interpreted as the probability of A and B occurring together is equal to the probability of A occurring given that B has occurred, multiplied by the probability of B occurring.

So, both choices B and C are incorrect because they don't use the conditional probability formula correctly.

Option A is also incorrect because it asks for the probability of being satisfied with marriage given satisfaction with job, instead of asking for the probability of satisfaction with both.

Therefore, the correct answer is D, as it represents the correct formula to use.

Question 3

The probability that an individual is satisfied with his marriage (event A)and satisfied with his job (event B)is an example of
A _____.
A)joint probability
B)conditional probability
C)marginal probability
D)mutually exclusive probability

Accepted Answer

Joint probability is the probability of the intersection of two or more events occurring simultaneously. In this case, the intersection of being satisfied with one's marriage and job is the joint probability.

Question 4

Sampling without replacement causes the probability of randomly selecting additional cases from that population to____.
A)stay the same
B)increase
C)decrease

Accepted Answer

When we sample without replacement, we are reducing the size of the population available for selection with each draw. This means that the probability of randomly selecting additional cases from that population decreases as the population size continues to shrink.

Question 5

A(n)_____ of a set of objects or events is an ordered sequence.
A)enumeration
B)combination
C)permutation
D)manipulation

Accepted Answer

A permutation is an ordered arrangement (sequence) of objects or events. An enumeration is a simple count of objects or events. A combination is a selection of objects without regards to order. Manipulation is a general term that does not specifically relate to ordering objects or events.

Question 6

In a binomial probability calculation,there are ____ possible outcomes.
A)many
B)N!
C)two
D)N!/r!

Accepted Answer

Binomial probability calculations only have two possible outcomes, success or failure.

Question 7

Even though two events are related (nonindependent),this does not necessarily mean that:
A)one is dependent on the other
B)one causes the other
C)the joint probability is 0
D)a and c

Accepted Answer

Nonindependence between two events means that they are statistically related, but it does not necessarily indicate a causal relationship or result in a joint probability of 0. Therefore, options A and D are incorrect. Option B is the best choice because it acknowledges that nonindependence does not necessarily imply causation, which is an important distinction to make in statistical analysis.

Question 8

Suppose you wanted a rat to learn a maze which included 3 choice points and each choice included 3 different directions.Assume only 1 choice can be correct at a time.What is the probability of a rat finding the goal without any errors? A)3! B)27 C)1/9 D).333³

Accepted Answer

The probability of the rat making the correct choice at each of the 3 choice points is 1/3. Therefore, the probability of making all correct choices is (1/3) * (1/3) * (1/3) = (1/3)^3 = 0.333^3.

Question 9

A permutation of a set of objects or events ____.
A)is an ordered sequence
B)is a sequence in which order doesn't matter
C)is a random selection of events
D)has fewer events than a combination

Accepted Answer

A permutation is an ordered sequence in which the arrangement matters. The order in which the objects or events appear is important, and changing the order will result in a different permutation.

Question 10

Suppose you are asked to toss 10 dimes and observe the number of heads.What is the likelihood of observing exactly 0 heads?
A).001
B).50
C)0
D)1.0

Accepted Answer

The likelihood of observing exactly 0 heads when tossing 10 dimes is calculated as (1/2)^10, which equals approximately 0.001.

Question 11

In the case of sampling _____,the outcome of the first random selection in no way affects the outcome of the second random selection.
A)without replacement
B)with replacement
C)with correction for continuity
D)without error

Accepted Answer

With replacement sampling means that each item in the population has the same chance of being selected multiple times. Therefore, the outcome of the first selection does not affect the outcome of subsequent selections.

Question 12

In a horse race,people are allowed to bet on which horses will finish a race in positions 1,2,or 3.If the field contained 7 horses,how many ways can 3 horses finish in the three positions?
A)7!
B)210
C)35
D)3

Accepted Answer

The number of ways to arrange 3 horses out of 7 in the top 3 positions is given by permutations: 7P3 = 7! / (7-3)! = 7 x 6 x 5 = 210.

Question 13

In general notation,the probability of observing at least one of event A and event B is:
A).50
B)p(A or B)= p(A)+ p(B)
C)p(A or B)= p(A)+ p(B)+ p(A,B)
D)p(A or B)= p(A)+ p(B)- p(A,B)

Accepted Answer

The correct formula for the probability of observing at least one of event A and event B is p(A or B)= p(A)+ p(B)- p(A,B). This is because if we were to add p(A) and p(B), we would be double-counting the probability of the intersection, p(A,B), leading to an overestimation of the total probability. Therefore, D is the best choice.

Question 14

Using the binomial expression to compute a probability requires ____.
A)a sequence of n independent trials
B)more than 2 outcomes
C)that the probability of success = .5
D)that the probability of failure = 0

Accepted Answer

The binomial expression is used to calculate the probability of a certain number of successes in a sequence of n independent trials, where each trial has the same probability of success.

Question 15

A set of objects that are arranged such that the internal order is irrelevant is called a ____.
A)combination
B)binomial root
C)permutation
D)simple event

Accepted Answer

A combination is a selection of objects from a set where order is not relevant, which matches the description given in the question. Permutations involve arrangements where order does matter, so it is not the best choice for this question. Binomial roots and simple events are not relevant to the concept of arranging objects.

Question 16

A counting rule that involves a set of objects of events in an ordered sequence is called a ____.
A)combination
B)conditional rule
C)binomial
D)permutation

Accepted Answer

A permutation involves an ordered sequence, where the order of the elements matters. A combination involves a set of objects or events where the order does not matter. A binomial involves two outcomes or events, such as success or failure. A conditional rule involves a probability rule where the probability of one event is affected by the occurrence of another event. Since the question specifically mentions an ordered sequence, the best choice is D, permutation.

Question 17

A combination of a set of objects or events is a sequence in which the internal ordering of elements is:
A)systematic
B)predetermined
C)important
D)irrelevant

Accepted Answer

The question is asking about the internal ordering of elements. If the ordering is irrelevant, it means that the sequence can be arranged in any way without changing the meaning or importance of the set of objects or events. Therefore, the best answer is D.

Question 18

The process of randomly selecting a case,taking some measurement of interest,and then returning the case to the population is called:
A)sampling without replacement
B)sampling with replacement
C)sampling without error
D)sampling with error

Accepted Answer

Sampling with replacement involves randomly selecting a case, taking a measurement of interest, and then returning the case to the population. This allows for the case to be selected multiple times, potentially increasing the representativeness and reducing bias in the sample. Sampling without replacement, on the other hand, involves selecting a case and not returning it to the population, which can lead to a biased sample. Sampling without error and with error are not commonly used terms in statistics.

Question 19

There are 6 students running for president at state college.The top 2 candidates are always declared winners and a run-off election is held to determine which of the two is the president.How many ways could 2 students be selected from among the first 6? A)30 B)6!/2! C)15 D)6³

Accepted Answer

The number of ways to select 2 students from 6 is given by 6 choose 2 which is equal to 15. Therefore, the answer is C.

Question 20

A therapist claims that a particular technique has been successful in the treatment of eating disorders.You find out that only 7 out of 10 clients were actually helped.What is the probability of observing 7 successes if the probability of success = .5?
A).7
B).5
C).117
D).77

Accepted Answer

The probability of success is 0.5, and the therapist treated 10 clients. The probability of observing exactly 7 successes in a sample of 10 with a success probability of 0.5 is calculated using the binomial distribution formula: P(X=7) = (10 choose 7) * 0.5^7 * 0.5^3 = 0.117. Therefore, the probability is 0.117 or 11.7%.

Quiz 6: Probability

The likelihood of observing each of two events is referred to as a:

Let event A be "satisfied with one's marriage" and event B be "satisfied with one's job.The probability that someone is satisfied with both his marriage and his job is equal to:

The probability that an individual is satisfied with his marriage (event A) and satisfied with his job (event B) is an example of A _____.

Sampling without replacement causes the probability of randomly selecting additional cases from that population to____.

A(n) _____ of a set of objects or events is an ordered sequence.

In a binomial probability calculation,there are ____ possible outcomes.

Even though two events are related (nonindependent) ,this does not necessarily mean that:

Suppose you wanted a rat to learn a maze which included 3 choice points and each choice included 3 different directions.Assume only 1 choice can be correct at a time.What is the probability of a rat finding the goal without any errors?

A permutation of a set of objects or events ____.

Suppose you are asked to toss 10 dimes and observe the number of heads.What is the likelihood of observing exactly 0 heads?

In the case of sampling _____,the outcome of the first random selection in no way affects the outcome of the second random selection.

In a horse race,people are allowed to bet on which horses will finish a race in positions 1,2,or 3.If the field contained 7 horses,how many ways can 3 horses finish in the three positions?

In general notation,the probability of observing at least one of event A and event B is:

Using the binomial expression to compute a probability requires ____.

A set of objects that are arranged such that the internal order is irrelevant is called a ____.

A counting rule that involves a set of objects of events in an ordered sequence is called a ____.

A combination of a set of objects or events is a sequence in which the internal ordering of elements is:

The process of randomly selecting a case,taking some measurement of interest,and then returning the case to the population is called:

There are 6 students running for president at state college.The top 2 candidates are always declared winners and a run-off election is held to determine which of the two is the president.How many ways could 2 students be selected from among the first 6?

A therapist claims that a particular technique has been successful in the treatment of eating disorders.You find out that only 7 out of 10 clients were actually helped.What is the probability of observing 7 successes if the probability of success = .5?