Quantitative Methods 【Reading 8】Sample normal, market, percent, next

ikoreaii

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%.

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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%.

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What is the probability of a bull market next year?

A) 20%.

B) 50%.

C) 32%.

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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%.

ikoreaii

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

A) current ratio.

B) most recent closing price.

C) stock symbol.

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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.

ikoreaii

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

A) 0.50.

B) 0.00.

C) Cannot be determined from the information given.

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

ikoreaii

Which of the following statements about probability is most accurate?

A) An outcome is the calculated probability of an event.

B) A conditional probability is the probability that two or more events will happen concurrently.

C) An event is a set of one or more possible values of a random variable.

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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.

ikoreaii

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

A) mutually exclusive.

B) statistically independent.

C) collectively exhaustive.

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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.

ikoreaii

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%.

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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%.

ikoreaii

Which of the following is an a priori probability?

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

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

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

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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&P500 for example, the a priori probability of selecting an airline stock would be that number divided by 500.

ikoreaii

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

A) a priori probability.

B) past lottery history.

C) the best estimate of the Department of Gaming.

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

ikoreaii

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) 20%.

B) 1 to 5.

C) 1 to 4.

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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.

ikoreaii

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 Ex equals 1 if the events are mutually exclusive and exhaustive.