答案和详解如下：

6、Thomas Baynes has applied to both Harvard and Yale. Baynes has determined that the probability of getting into Harvard is 25 percent and the probability of getting into Yale (his father’s alma mater) is 42 percent. Baynes has also determined that the probability of being accepted at both schools is 2.8 percent. What is the probability of Baynes being accepted at either Harvard or Yale, but not both?

A)   64.2%.

B)   7.7%.

C)   10.5%.

D)   67.0%.

The correct answer was A)

Using the addition rule, the probability of being accepted at Harvard or Yale, but not both, is equal to: P(Harvard) + P(Yale) – P(Harvard and Yale) = 0.25 + 0.42 – 0.028 = 0.642 or 64.2%.

7、Jessica Fassler, options trader, recently wrote two put options on two different underlying stocks (AlphaDog Software and OmegaWolf Publishing), both with a strike price of $11.50. The probabilities that the prices of AlphaDog and OmegaWolf stock will decline below the strike price are 65 percent and 47 percent, respectively. The probability that at least one of the put options will fall below the strike price is approximately:

A)   0.31.

B)   1.00.

C)   0.81.

D)   0.47.

The correct answer was C)    

We calculate the probability that at least one of the options will fall below the strike price using the addition rule for probabilities (A represents AlphaDog, O represents OmegaWolf):

P(A or O) = P(A) + P(O) – P(A and O), where P(A and O) = P(A) * P(O)
P(A or O) = 0.65 + 0.47 – (0.65 * 0.47) = approximately 0.81

8、The following table summarizes the results of a poll taken of CEO's and analysts concerning the economic impact of a pending piece of legislation:

What is the probability that a randomly selected individual from this group will be either an analyst or someone who thinks this legislation will have a positive impact on the economy?

A)   0.75.

B)   0.80.

C)   0.90.

D)   0.85.

The correct answer was D)

There are 130 total analysts and 40 CEOs who think it will have a positive impact. (130 + 40)/200 = 0.85.

9、The following table summarizes the results of a poll taken of CEO's and analysts concerning the economic impact of a pending piece of legislation:

What is the probability that a randomly selected individual from this group will be an analyst that thinks that the legislation will have a positive impact on the economy?

A)   0.45.

B)   0.30.

C)   0.35.

D)   0.40.

The correct answer was C)

70 analysts / 200 individuals = 0.35.