Q4. 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)   0.76.

B)   0.92.

C)   0.06.

Q5. If the probability of an event is 0.20, what are the odds against the event occurring?

A)   Five to one.

B)   Four to one.

C)   One to four.

Q6. If the odds against an event occurring are twelve to one, what is the probability that it will occur?

A)   0.0833.

B)   0.0769.

C)   0.9231.

答案和详解如下：

Q4. 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)   0.76.

B)   0.92.

C)   0.06.

Correct answer is B)

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%.

Q5. If the probability of an event is 0.20, what are the odds against the event occurring?

A)   Five to one.

B)   Four to one.

C)   One to four.

Correct answer is B)

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.

Q6. If the odds against an event occurring are twelve to one, what is the probability that it will occur?

A)   0.0833.

B)   0.0769.

C)   0.9231.

Correct answer is B)

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.

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