答案和详解如下：

6、Which of the following sets of numbers does NOT meet the requirements for a set of probabilities?

A)   (0.50, 0.50).

B)   (0.25, 0.25, 0.25, 0.25).

C)   (0.10, 0.20, 0.30, 0.40).

D)   (0.10, 0.20, 0.30, 0.40, 0.50).

The correct answer was D)    

A set of probabilities must sum to one.

7、An empirical probability is one that is:

A)   determined by mathematical principles.

B)   derived from analyzing past data.

C)   determined based on the judgment of the researcher.

D)   supported by formal reasoning.

The correct answer was B)    

An empirical probability is one that is derived from analyzing past data. For example, a basketball player has scored at least 22 points in each of the season’s 18 games. Therefore, there is a high probability that he will score 22 points in tonight’s game.

8、Which of the following statements about the defining properties of probability is TRUE?

A)   The probability of any event is between 0 and 1, exclusive.

B)   The sum of the probabilities of events E₁ though E_x equals one if the events are mutually exclusive or exhaustive.

C)   Mutually exclusive means that events share outcomes.

D)   If the device that generates an event is not fair, the events can be mutually exclusive and exhaustive.

The correct answer was D)

Even if the device that generates an event is not fair, the events can be mutually exclusive and exhaustive. Consider a standard die with the possible outcomes of 1,2,3,4,5 and 6. The P(2 or 4 or 6) = 0.50 and P(1 or 3 or 5) = 0.50, and thus the probabilities sum to 1 and are mutually exclusive and exhaustive. An unfair die would not change this.

The other statements are false. The probability of any event is between 0 and 1, inclusive. It is possible that the probability of an event could equal 0 or 1, or any point in between. The sum of the probabilities of events E₁ though E_x equals 1 if the events are mutually exclusive and exhaustive. Mutually exclusive means that events do not share outcomes.

9、Last year, the average salary increase for poultry research assistants was 2.5%. Of the 10,000 poultry research assistants, 2,000 received raises in excess of this amount. The odds that a randomly selected poultry research assistant received a salary increase in excess of 2.5% are:

A)   1 to 5.

B)   20%.

C)   1 to 4.

D)   25%.

The correct answer was C)    

For event “E,” the probability stated as odds is: P(E) / [1 – P(E)]. Here, the probability that a poultry research assistant received a salary increase in excess of 2.5% = 2,000 / 10,000 = 0.20, or 1/5 and the odds are (1/5) / [1 – (1/5)] = 1/4, or 1 to 4.

6、Which of the following sets of numbers does NOT meet the requirements for a set of probabilities?

A)   (0.50, 0.50).

B)   (0.25, 0.25, 0.25, 0.25).

C)   (0.10, 0.20, 0.30, 0.40).

D)   (0.10, 0.20, 0.30, 0.40, 0.50).

7、An empirical probability is one that is:

A)   determined by mathematical principles.

B)   derived from analyzing past data.

C)   determined based on the judgment of the researcher.

D)   supported by formal reasoning.

8、Which of the following statements about the defining properties of probability is TRUE?

A)   The probability of any event is between 0 and 1, exclusive.

B)   The sum of the probabilities of events E₁ though E_x equals one if the events are mutually exclusive or exhaustive.

C)   Mutually exclusive means that events share outcomes.

D)   If the device that generates an event is not fair, the events can be mutually exclusive and exhaustive.

9、Last year, the average salary increase for poultry research assistants was 2.5%. Of the 10,000 poultry research assistants, 2,000 received raises in excess of this amount. The odds that a randomly selected poultry research assistant received a salary increase in excess of 2.5% are:

A)   1 to 5.

B)   20%.

C)   1 to 4.

D)   25%.