1、If the outcome of event A is not affected by event B, then events A and B are said to be:

A)   mutually exclusive.

B)   statistically independent.

C)   collectively exhaustive.

D)   conditionally dependent.

2、A company says that whether it increases its dividends depends on whether its earnings increase. From this we know:

A)   P(both dividend increase and earnings increase) = P(dividend increase).

B)   P(dividend increase or earnings increase) = P(both dividend and earnings increase).

C)   P(earnings increase | dividend increase) is not equal to P(earnings increase).

D)   P(dividend increase | earnings increase) is not equal to P(earnings increase).

3、If X and Y are independent events, which of the following must be TRUE?

A)   P(X or Y) = P(X) + P(Y).

B)   X and Y cannot occur together.

C)   P(X or Y) = (P(X)) * (P(Y)).

D)   P(X | Y) = P(X).

答案和详解如下：

1、If the outcome of event A is not affected by event B, then events A and B are said to be:

A)   mutually exclusive.

B)   statistically independent.

C)   collectively exhaustive.

D)   conditionally dependent.

The correct answer was B)

If the outcome of one event does not influence the outcome of another, then the events are independent.

2、A company says that whether it increases its dividends depends on whether its earnings increase. From this we know:

A)   P(both dividend increase and earnings increase) = P(dividend increase).

B)   P(dividend increase or earnings increase) = P(both dividend and earnings increase).

C)   P(earnings increase | dividend increase) is not equal to P(earnings increase).

D)   P(dividend increase | earnings increase) is not equal to P(earnings increase).

The correct answer was C)    

If two events A and B are dependent, then the conditional probabilities of P(A|B) and P(B|A) will not equal their respective unconditional probabilities (of P(A) and P(B), respectively). The other choices may or may not occur, e.g., P(A | B) = P(B) is possible but not necessary.

3、If X and Y are independent events, which of the following must be TRUE?

A)   P(X or Y) = P(X) + P(Y).

B)   X and Y cannot occur together.

C)   P(X or Y) = (P(X)) * (P(Y)).

D)   P(X | Y) = P(X).

The correct answer was D)

Note that events being independent means that they have no influence on each other. It does not necessarily mean that they are mutually exclusive. Accordingly, P(X or Y) = P(X) + P(Y) – P(X and Y). By the definition of independent events, P(X|Y) = P(X).