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标题: Reading 8: Probability Concepts-LOS f, (Part 2)习题精选 [打印本页]
作者: bmaggie    时间: 2010-4-12 14:04     标题: [2010]Session 2:-Reading 8: Probability Concepts-LOS f, (Part 2)习题精选

Session 2: Quantitative Methods: Basic Concepts
Reading 8: Probability Concepts

LOS f, (Part 2): Calculate and interpret the probability that at least one of two events will occur, given the probability of each and the joint probability of the two events.

 

 

 

 

A firm holds two $50 million bonds with call dates this week.

The probability that at least one of the bonds will be called is closest to:

 

A)
 0.86.
B)
 0.24.
C)
 0.50.

作者: bmaggie    时间: 2010-4-12 14:04

 

A firm holds two $50 million bonds with call dates this week.

The probability that at least one of the bonds will be called is closest to:

A)
 0.86.
B)
 0.24.
C)
 0.50.


We calculate the probability that at least one of the bonds will be called using the addition rule for probabilities:

P(A or B) = P(A) + P(B) – P(A and B), where P(A and B) = P(A) × P(B)

P(A or B) = 0.80 + 0.30 – (0.8 × 0.3) = 0.86

作者: bmaggie    时间: 2010-4-12 14:06

There is a 50% chance that the Fed will cut interest rates tomorrow. On any given day, there is a 67% chance the DJIA will increase. On days the Fed cuts interest rates, the probability the DJIA will go up is 90%. What is the probability that tomorrow the Fed will cut interest rates or the DJIA will go up?

A)
 0.72.
B)
 0.33.
C)
 0.95.

作者: bmaggie    时间: 2010-4-12 14:06

There is a 50% chance that the Fed will cut interest rates tomorrow. On any given day, there is a 67% chance the DJIA will increase. On days the Fed cuts interest rates, the probability the DJIA will go up is 90%. What is the probability that tomorrow the Fed will cut interest rates or the DJIA will go up?

A)
 0.72.
B)
 0.33.
C)
 0.95.


This requires the addition formula. From the information: P(cut interest rates) = 0.50 and P(DJIA increase) = 0.67, P(DJIA increase | cut interest rates) = 0.90. The joint probability is 0.50 × 0.90 = 0.45. Thus P (cut interest rates or DJIA increase) = 0.50 + 0.67 ? 0.45 = 0.72.

作者: bmaggie    时间: 2010-4-12 14:10

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)
 1.00.
C)
 0.81.

作者: bmaggie    时间: 2010-4-12 14:10

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)
 1.00.
C)
 0.81.

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

作者: bmaggie    时间: 2010-4-12 14:10

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)
 64.2%.
B)
 7.7%.
C)
 10.5%.

作者: bmaggie    时间: 2010-4-12 14:11

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)
 64.2%.
B)
 7.7%.
C)
 10.5%.


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%.

作者: bmaggie    时间: 2010-4-12 14:11

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)

0.85.

B)

0.70.

C)

0.55.

作者: bmaggie    时间: 2010-4-12 14:11

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)

0.85.

B)

0.70.

C)

0.55.



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.

作者: zaestau    时间: 2010-4-26 23:30

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