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发表于 2011-3-1 15:04 | 只看该作者

Reading 8: Probability Concepts-LOS a 习题精选

2011, center, events, style
Session 2: Quantitative Methods: Basic Concepts
Reading 8: Probability Concepts

LOS a: Define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events.

 

 

There is a 40% chance that the economy will be good next year and a 60% chance that it will be bad. If the economy is good, there is a 50 percent chance of a bull market, a 30% chance of a normal market, and a 20% chance of a bear market. If the economy is bad, there is a 20% chance of a bull market, a 30% chance of a normal market, and a 50% chance of a bear market.

What is the joint probability of a good economy and a bull market?

A)
 50%.
B)
 20%.
C)
 12%.

Joint probability is the probability that both events, in this case the economy being good and the occurrence of a bull market, happen at the same time. Joint probability is computed by multiplying the individual event probabilities together: (0.40) × (0.50) = 0.20 or 20%.

What is the probability of a bull market next year?

A)
 32%.
B)
 20%.
C)
 50%.

Because a good economy and a bad economy are mutually exclusive, the probability of a bull market is the sum of the joint probabilities of (good economy and bull market) and (bad economy and bull market): ((0.40) × (0.50)) + ((0.60) × (0.20)) = 0.32 or 32%.

 

 

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For a stock, which of the following is least likely a random variable? Its:

A)
 stock symbol.
B)
 current ratio.
C)
 most recent closing price.

A random variable must be a number. Sometimes there is an obvious method for assigning a number, such as when the random variable is a number itself, like a P/E ratio. A stock symbol of a randomly selected stock could have a number assigned to it like the number of letters in the symbol. The symbol itself cannot be a random variable.

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If two events are mutually exclusive, the probability that they both will occur at the same time is:

A)
 0.50.
B)
 Cannot be determined from the information given.
C)
 0.00.

If two events are mutually exclusive, it is not possible to occur at the same time.  Therefore, the P(A∩B) = 0.

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Which of the following statements about probability is most accurate?

A)
 An outcome is the calculated probability of an event.
B)
 An event is a set of one or more possible values of a random variable.
C)
 A conditional probability is the probability that two or more events will happen concurrently.

Conditional probability is the probability of one event happening given that another event has happened. An outcome is the numerical result associated with a random variable.

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If event A and event B cannot occur simultaneously, then events A and B are said to be:

A)
 statistically independent.
B)
 collectively exhaustive.
C)
 mutually exclusive.

If two events cannot occur together, the events are mutually exclusive. A good example is a coin flip: heads AND tails cannot occur on the same flip.

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In any given year, the chance of a good year is 40%, an average year is 35%, and the chance of a bad year is 25%. What is the probability of having two good years in a row?

A)
 10.00%.
B)
 16.00%.
C)
 8.75%.

The joint probability of independent events is obtained by multiplying the probabilities of the individual events together: (0.40) × (0.40) = 0.16 or 16%.

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