Reading 8: Probability Concepts-LOS f, (Part 2)习题精选 interpret, div, class, center, events

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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 Bond A will be called is 0.80.
• The probability that Bond B will be called is 0.30.

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

 

A) 0.86.

B) 0.24.

C) 0.50.

bmaggie

 

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

• The probability that Bond A will be called is 0.80.
• The probability that Bond B will be called is 0.30.

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

A) 0.86.

B) 0.24.

C) 0.50.

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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

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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.

bmaggie

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.

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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.

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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.

bmaggie

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.

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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

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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%.

bmaggie

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%.

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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%.

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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.

bmaggie

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.

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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.