Q1. If X and Y are independent events, which of the following is most accurate?

A)   P(X or Y) = (P(X)) × (P(Y)).

B)   P(X or Y) = P(X) + P(Y).

C)   P(X | Y) = P(X).

Q2. 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(earnings increase | dividend increase) is not equal to P(earnings increase).

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

Q3. If the outcome of event A is not affected by event B, then events A and B are said to be:

A)   conditionally dependent.

B)   statistically independent.

C)   mutually exclusive.

答案和详解如下：

Q1. If X and Y are independent events, which of the following is most accurate?

A)   P(X or Y) = (P(X)) × (P(Y)).

B)   P(X or Y) = P(X) + P(Y).

C)   P(X | Y) = P(X).

Correct answer is C)

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).

Q2. 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(earnings increase | dividend increase) is not equal to P(earnings increase).

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

Correct answer is B)

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). Both remaining choices may or may not occur, e.g., P(A | B) = P(B) is possible but not necessary.

Q3. If the outcome of event A is not affected by event B, then events A and B are said to be:

A)   conditionally dependent.

B)   statistically independent.

C)   mutually exclusive.

Correct answer is B)

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

谢谢