Question 1

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 answer of Suppose you wanted a rat to learn...

Question 2

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 two or more events occurring together. In this case, the event of being satisfied with marriage (A) and the event of being satisfied with job (B) are occurring simultaneously, making it an example of joint probability.

Question 3

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 compute the probability of a certain number of successes in a specific number of independent trials. Therefore, A is the correct choice as it requires a sequence of n independent trials.

Question 4

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 set of objects where the order does not matter. This is different from a permutation, where the order does matter. A binomial root and simple event are not mathematical concepts related to arrangements of objects.

Question 5

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 is a counting rule that involves a set of objects or events in an ordered sequence, while a combination does not account for order. A conditional rule is a rule based on specific conditions or probability, and binomial is a type of probability distribution. Therefore, the best choice for this question is D, permutation.

Question 6

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 likelihood of observing two events simultaneously is referred to as joint probability.

Question 7

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 of a set of objects or events. Enumeration refers to the act of counting or listing items, and manipulation refers to changing or altering objects or events. A combination does not involve order and refers to the number of ways to choose a subset of objects from a larger set. Therefore, the best choice is C, permutation.

Question 8

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 2 students could be selected from among 6 is given by the combination formula: C(6,2) = 6!/(2!4!) = 15.

Question 9

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 is when each case has an equal chance of being selected for each measurement, and after each selection, the case is returned to the population. This allows for the possibility of a case being selected multiple times, and is the best choice for ensuring randomness in the selection process. Sampling without replacement would not allow for the same case to be selected multiple times, which may skew the results. Sampling with error is not a recognized term in sampling methodology. Sampling without error implies a perfect sampling process, which is not possible in practice.

Question 10

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

Just because two events are related, it does not mean that one causes the other. There could be other factors influencing both events.

Question 11

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

Option D is the correct formula for finding the probability of observing at least one of event A and event B. It states that the probability of A or B happening equals the sum of their individual probabilities minus the probability of both A and B happening together. This accounts for any overlap between the two events and ensures that it is not counted twice in the final probability.

Question 12

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

Accepted Answer

A binomial probability calculation involves only two possible outcomes – success or failure.

Question 13

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 of someone being satisfied with both their marriage and job can be calculated using the formula: 
p(A,B) = p(A|B) * p(B)

Therefore, both choices B and C are relevant. 
Choice B (p(A,B)) represents the joint probability of both events occurring, and 
Choice C (p(B)*p(A|B)) represents the probability of event B occurring (satisfaction with the job) multiplied by the conditional probability of event A occurring given event B (i.e., the probability of being satisfied with one's marriage given that one is satisfied with their job).

Hence, the correct choice is D.

Question 14

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

Sampling without replacement reduces the size of the population available for future selections, thus decreasing the probability of randomly selecting additional cases.

Question 15

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 probability of getting heads on a single coin toss is 0.5, and the probability of getting tails (not heads) is also 0.5. For 10 dimes, the probability of getting exactly 0 heads (meaning all tails) is $0.5^{10}$ = 0.0009765625, which rounds to 0.001.

Question 16

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

To find the number of ways 3 horses can finish in the top 3 positions out of a field of 7, we can use the formula for combinations: nCr = n! / (r!(n-r)!) where n is the total number of horses and r is the number of horses we want to select for the top three positions.

In this case, we want to select 3 horses for the top 3 positions out of 7 horses, so we can calculate:

7C3 = 7! / (3!(7-3)!) = 7! / (3!4!) = (7 x 6 x 5) / (3 x 2 x 1) = 35 x 2 = 70

Therefore, there are 70 ways for 3 horses to finish in the top 3 positions out of a field of 7. The correct answer is B) 210, which is not one of the choices, so the closest choice is C) 35, which is the number of combinations for selecting 2 horses out of 7.

Question 17

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

This question requires the use of the binomial distribution formula to calculate the probability of observing 7 successes out of 10 trials with a probability of success of .5. The formula is P(X=7) = (10 choose 7)*(0.5)^7*(0.5)^3, where (10 choose 7) is the number of ways of selecting 7 successes from 10 trials. Using a calculator or table, we find that (10 choose 7) = 120. Plugging this into the formula, we get P(X=7) = 120*(0.5)^10 = 0.117. Therefore, the probability of observing 7 successes if the probability of success is .5 is 0.117 or approximately 11.7%. Choice C is the only option that matches this calculation.

Question 18

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 referring to the internal ordering of elements, meaning the order in which they appear in the sequence. If the ordering is irrelevant, it means that each element can appear in any position without changing the overall meaning or purpose of the sequence. Therefore, the best choice is D) irrelevant.

Question 19

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 selection is independent of the previous selections, so the outcome of the first selection will not affect the outcome of the second selection. Therefore, option B is the correct answer.

Question 20

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, meaning that the arrangement or order of the objects or events matters in defining that permutation. For example, the arrangement ABC is a different permutation from BAC or CAB.

Quiz 6: Probability

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?

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

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 ____.

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

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

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?

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

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

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

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

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:

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

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

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

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

A permutation of a set of objects or events ____.