Reading 8: Probability Concepts-LOS c习题精选 center, border, against, occurring, 2010

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

LOS c: State the probability of an event in terms of odds for or against the event.

 

 

 

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

A) One to nine.

B) One to ten.

C) Nine to one.

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

A) One to nine.

B) One to ten.

C) Nine to one.

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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.

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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) 1.99.

C) 0.50.

bmaggie

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) 1.99.

C) 0.50.

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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.

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

A) One to four.

B) Four to one.

C) Five to one.

bmaggie

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

A) One to four.

B) Four to one.

C) Five to one.

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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.

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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.

bmaggie

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%.

bmaggie

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

A) Five to one.

B) One to four.

C) Four to one.

bmaggie

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

A) Five to one.

B) One to four.

C) Four to one.

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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.