Q6. If event A and event B cannot occur simultaneously, then events A and B are said to be:

A)   statistically independent.

B)   collectively exhaustive.

C)   mutually exclusive.

Q7. 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)  16.00%.

B)  10.00%.

C)  8.75%.

答案和详解如下：

Q6. If event A and event B cannot occur simultaneously, then events A and B are said to be:

A)   statistically independent.

B)   collectively exhaustive.

C)   mutually exclusive.

Correct answer is C)

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.

Q7. 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)  16.00%.

B)  10.00%.

C)  8.75%.

Correct answer is A)

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%.