Reading 8: Probability Concepts-LOS b 习题精选 2011, following, defining, border, center

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Session 2: Quantitative Methods: Basic Concepts
Reading 8: Probability Concepts

LOS b: Explain the two defining properties of probability and distinguish among empirical, subjective, and a priori probabilities.

 

 

Which of the following is an a priori probability?

A) For a stock, based on prior patterns of up and down days, the probability of the stock having a down day tomorrow.

B) The probability the Fed will lower interest rates prior to the end of the year.

C) On a random draw, the probability of choosing a stock of a particular industry from the S& 500.

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A priori probability is based on formal reasoning and inspection. Given the number of stocks in the airline industry in the S&500 for example, the a priori probability of selecting an airline stock would be that number divided by 500.

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Each lottery ticket discloses the odds of winning. These odds are based on:

A) past lottery history.

B) the best estimate of the Department of Gaming.

C) a priori probability.

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An a priori probability is based on formal reasoning rather than on historical results or subjective opinion.

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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 4.

B) 20%.

C) 1 to 5.

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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.

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Which of the following statements about the defining properties of probability is most accurate?

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

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

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

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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.

Both remaining 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.

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An empirical probability is one that is:

A) supported by formal reasoning.

B) determined by mathematical principles.

C) derived from analyzing past data.

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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.

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

A) (0.50, 0.50).

B) (0.10, 0.20, 0.30, 0.40).

C) (0.10, 0.20, 0.30, 0.40, 0.50).

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A set of probabilities must sum to one.

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Which of the following is an empirical probability?

A) For a stock, based on prior patterns of up and down days, the probability of the stock having a down day tomorrow.

B) The probability the Fed will lower interest rates prior to the end of the year.

C) On a random draw, the probability of choosing a stock of a particular industry from the S& 500 based on the number of firms.

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There are three types of probabilities: a priori, empirical, and subjective. An empirical probability is calculated by analyzing past data.