ikoreaii

Let A and B be two mutually exclusive events with P(A) = 0.40 and P(B) = 0.20. Therefore:

A) P(B|A) = 0.20.

B) P(A and B) = 0.

C) P(A and B) = 0.08.

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If the two evens are mutually exclusive, the probability of both ocurring is zero.

ikoreaii

If the odds against an event occurring are twelve to one, what is the probability that it will occur?

A) 0.0833.

B) 0.9231.

C) 0.0769.

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If the probability against the event occurring is twelve to one, this means that in thirteen occurrences of the event, it is expected that it will occur once and not occur twelve times. The probability that the event will occur is then: 1/13 = 0.0769.

ikoreaii

If the probability of an event is 0.20, what are the odds against the event occurring?

A) Four to one.

B) Five to one.

C) One to four.

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The answer can be determined by dividing the probability of the event by the probability that it will not occur: (1/5) / (4/5) = 1 to 4. The probability against the event occurring is four to one, i.e. in five occurrences of the event, it is expected that it will occur once and not occur four times.

ikoreaii

A company has two machines that produce widgets. An older machine produces 16% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine employs a superior production process such that it produces three times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is NOT defective?

A) 0.92.

B) 0.76.

C) 0.06.

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The problem is just asking for the conditional probability of a defective widget given that it was produced by the new machine. Since the widget was produced by the new machine and not selected from the output randomly (if randomly selected, you would not know which machine produced the widget), we know there is an 8% chance it is defective. Hence, the probability it is not defective is the complement, 1 – 8% = 92%.

ikoreaii

At a charity fundraiser there have been a total of 342 raffle tickets already sold. If a person then purchases two tickets rather than one, how much more likely are they to win?

A) 2.10.

B) 0.50.

C) 1.99.

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If you purchase one ticket, the probability of your ticket being drawn is 1/343 or 0.00292. If you purchase two tickets, your probability becomes 2/344 or 0.00581, so you are 0.00581 / 0.00292 = 1.99 times more likely to win.

ikoreaii

If the probability of an event is 0.10, what are the odds for the event occurring?

A) One to ten.

B) Nine to one.

C) One to nine.

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The answer can be determined by dividing the probability of the event by the probability that it will not occur: (1/10) / (9/10) = 1 to 9. The probability of the event occurring is one to nine, i.e. in ten occurrences of the event, it is expected that it will occur once and not occur nine times.

ikoreaii

Which of the following is an empirical probability?

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

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

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

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

ikoreaii

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

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

B) (0.50, 0.50).

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

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A set of probabilities must sum to one.

ikoreaii

An empirical probability is one that is:

A) derived from analyzing past data.

B) supported by formal reasoning.

C) determined by mathematical principles.

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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.

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.