1215

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.

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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.

1215

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) 0.33.

B) 0.72.

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.

1215

If the probability of both a new Wal-Mart and a new Wendy’s being built next month is 68% and the probability of a new Wal-Mart being built is 85%, what is the probability of a new Wendy’s being built if a new Wal-Mart is built?

A) 0.60.

B) 0.80.

C) 0.70.

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P(AB) = P(A|B) × P(B)

0.68 / 0.85 = 0.80

1215

The probability of a new Wal-Mart being built in town is 64%. If Wal-Mart comes to town, the probability of a new Wendy’s restaurant being built is 90%. What is the probability of a new Wal-Mart and a new Wendy’s restaurant being built?

A) 0.576.

B) 0.675.

C) 0.306.

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P(AB) = P(A|B) × P(B)

The probability of a new Wal-Mart and a new Wendy’s is equal to the probability of a new Wendy’s “if Wal-Mart” (0.90) times the probability of a new Wal-Mart (0.64). (0.90)(0.64) = 0.576.

1215

 

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

1215

In a given portfolio, half of the stocks have a beta greater than one. Of those with a beta greater than one, a third are in a computer-related business. What is the probability of a randomly drawn stock from the portfolio having both a beta greater than one and being in a computer-related business?

A) 0.667.

B) 0.333.

C) 0.167.

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This is a joint probability. From the information: P(beta > 1) = 0.500 and P(comp. stock | beta > 1) = 0.333. Thus, the joint probability is the product of these two probabilities: (0.500) × (0.333) = 0.167.

1215

Data shows that 75 out of 100 tourists who visit New York City visit the Empire State Building. It rains or snows in New York City one day in five. What is the joint probability that a randomly choosen tourist visits the Empire State Building on a day when it neither rains nor snows?

A) 95%.

B) 60%.

C) 15%.

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A joint probability is the probability that two events occur when neither is certain or a given. Joint probability is calculated by multiplying the probability of each event together. (0.75) × (0.80) = 0.60 or 60%.

1215

Helen Pedersen has all her money invested in either of two mutual funds (A and B). She knows that there is a 40% probability that fund A will rise in price and a 60% chance that fund B will rise in price if fund A rises in price. What is the probability that both fund A and fund B will rise in price?

A) 1.00.

B) 0.40.

C) 0.24.

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P(A) = 0.40, P(B|A) = 0.60. Therefore, P(A?B) = P(A)P(B|A) = 0.40(0.60) = 0.24.