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

A)   Five to one.

B)   One to five.

C)   Four to one.

D)   One to four.

2、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)   1.99.

B)   2.10.

C)   0.50.

D)   1.67.

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

A)   One to nine.

B)   Nine to one.

C)   Ten to one.

D)   One to ten.

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

A)   0.0769.

B)   0.0833.

C)   0.9167.

D)   0.9231.

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

A)   Four to one.

B)   One to four.

C)   Five to one.

D)   One to five.

6、A company has two machines that produce widgets. An older machine produces 16 percent defective widgets, while the new machine produces only 8 percent 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)   0.06.

C)   0.50.

D)   0.76.

答案和详解如下：

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

A)   Five to one.

B)   One to five.

C)   Four to one.

D)   One to four.

The correct answer was C)

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.

2、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)   1.99.

B)   2.10.

C)   0.50.

D)   1.67.

The correct answer was A)    

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.

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

A)   One to nine.

B)   Nine to one.

C)   Ten to one.

D)   One to ten.

The correct answer was A)    

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.

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

A)   0.0769.

B)   0.0833.

C)   0.9167.

D)   0.9231.

The correct answer was A)    

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.

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

A)   Four to one.

B)   One to four.

C)   Five to one.

D)   One to five.

The correct answer was A)    

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.

6、A company has two machines that produce widgets. An older machine produces 16 percent defective widgets, while the new machine produces only 8 percent 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)   0.06.

C)   0.50.

D)   0.76.

The correct answer was A)

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 percent chance it is defective. Hence, the probability it is not defective is the complement, 1 – 8% = 92%.