Q7. 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% and 47%, respectively. The probability that at least one of the put options will fall below the strike price is approximately:

A)   0.31.

B)   0.81.

C)   1.00.

Q8. Thomas Baynes has applied to both Harvard and Yale. Baynes has determined that the probability of getting into Harvard is 25% and the probability of getting into Yale (his father’s alma mater) is 42%. Baynes has also determined that the probability of being accepted at both schools is 2.8%. What is the probability of Baynes being accepted at either Harvard or Yale, but not both?

A)   7.7%.

B)   64.2%.

C)   10.5%.

Q9. An analyst has a list of 20 bonds of which 14 are callable, and five have warrants attached to them. Two of the callable bonds have warrants attached to them. If a single bond is chosen at random, what is the probability of choosing a callable bond or a bond with a warrant?

A)    0.70.

B)    0.85.

C)    0.55.

答案和详解如下：

Q7. 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% and 47%, respectively. The probability that at least one of the put options will fall below the strike price is approximately:

A)   0.31.

B)   0.81.

C)   1.00.

Correct answer is B)

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

Q8. Thomas Baynes has applied to both Harvard and Yale. Baynes has determined that the probability of getting into Harvard is 25% and the probability of getting into Yale (his father’s alma mater) is 42%. Baynes has also determined that the probability of being accepted at both schools is 2.8%. What is the probability of Baynes being accepted at either Harvard or Yale, but not both?

A)   7.7%.

B)   64.2%.

C)   10.5%.

Correct answer is B)

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%.

Q9. An analyst has a list of 20 bonds of which 14 are callable, and five have warrants attached to them. Two of the callable bonds have warrants attached to them. If a single bond is chosen at random, what is the probability of choosing a callable bond or a bond with a warrant?

A)    0.70.

B)    0.85.

C)    0.55.

Correct answer is B)

This requires the addition formula, P(callable) + P(warrants) – P(callable and warrants) = P(callable or warrants) = 14/20 + 5/20 – 2/20 = 17/20 = 0.85.

谢谢了 哈哈