6、Tully Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Tully’s economist has estimated the probability of each scenario as shown in the table below. Given this information, what is the expected return on portfolio A?
Scenario | Probability | Return on Portfolio A | Return on Portfolio B |
A | 15% | 17% | 19% |
B | 20% | 14% | 18% |
C | 25% | 12% | 10% |
D | 40% | 8% | 9% |
A) 11.55%.
B) 9.25%.
C) 10.75%.
D) 12.95%.
7、There is a 30 percent probability of rain this afternoon. There is a 10 percent probability of having an umbrella if it rains. What is the chance of it raining and having an umbrella?
A) 33%.
B) 9%.
C) 3%.
D) 40%.
8、Avery Scott, financial planner, recently obtained his CFA Charter and is considering multiple job offers. Scott devised the following four criteria to help him decide which offers to pursue most aggressively.
Criterion | % Expected to Meet the Criteria |
1. Within 75 miles of | 0.85 |
2. Employee size less than 50 | 0.50 |
3. Compensation package exceeding $100,000 | 0.30 |
4. Three weeks of vacation | 0.15 |
If Scott has 20 job offers and the probabilities of meeting each criterion are independent, how many are expected to meet all of his criteria? (Round to nearest whole number).
A) 0.
B) 1.
C) 3.
D) 5.
9、Which of the following is a joint probability? The probability that a:
A) company merges with another firm next year.
B) stock increases in value after an increase in interest rates has occurred.
C) stock either splits or is registered on the NYSE.
D) stock pays a dividend and splits next year.
10、A joint probability of A and B must always be:
A) less than or equal to the conditional probability of A given B.
B) greater than or equal to the conditional probability of A given B.
C) greater than or equal to than the probability of A or B.
D) less than the probability of A and the probability of B.
11、A very large company has equal amounts of male and female employees. If a random sample of four employees is selected, what is the probability that all four employees selected are female?
A) 0.0625.
B) 0.0256
C) 0.1600
D) 1.0000
答案和详解如下：
6、Tully Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Tully’s economist has estimated the probability of each scenario as shown in the table below. Given this information, what is the expected return on portfolio A?
Scenario | Probability | Return on Portfolio A | Return on Portfolio B |
A | 15% | 17% | 19% |
B | 20% | 14% | 18% |
C | 25% | 12% | 10% |
D | 40% | 8% | 9% |
A) 11.55%.
B) 9.25%.
C) 10.75%.
D) 12.95%.
The correct answer was A)
The expected return is equal to the sum of the products of the probabilities of the scenarios and their respective returns: = (0.15)(0.17) + (0.20)(0.14) + (0.25)(0.12) + (0.40)(0.08) = 0.1155 or 11.55%.
7、There is a 30 percent probability of rain this afternoon. There is a 10 percent probability of having an umbrella if it rains. What is the chance of it raining and having an umbrella?
A) 33%.
B) 9%.
C) 3%.
D) 40%.
The correct answer was C)
P(A) = 0.30. P(B|A) = 0.10. P(AB) = (0.30)(0.10) = 0.03 or 3%.
8、Avery Scott, financial planner, recently obtained his CFA Charter and is considering multiple job offers. Scott devised the following four criteria to help him decide which offers to pursue most aggressively.
Criterion | % Expected to Meet the Criteria |
1. Within 75 miles of | 0.85 |
2. Employee size less than 50 | 0.50 |
3. Compensation package exceeding $100,000 | 0.30 |
4. Three weeks of vacation | 0.15 |
If Scott has 20 job offers and the probabilities of meeting each criterion are independent, how many are expected to meet all of his criteria? (Round to nearest whole number).
A) 0.
B) 1.
C) 3.
D) 5.
The correct answer was A)
We will use the multiplication rule to calculate this probability.
P(1 & 2 & 3& 4) = P(1) * P(2) * P(3) * P(4)
= 0.85 * 0.50 * 0.30 * 0.15 = 0.019125
Number of offers expected to meet the criteria = 0.019125 * 20 = 0.3825, or 0.
9、Which of the following is a joint probability? The probability that a:
A) company merges with another firm next year.
B) stock increases in value after an increase in interest rates has occurred.
C) stock either splits or is registered on the NYSE.
D) stock pays a dividend and splits next year.
The correct answer was D)
A joint probability applies to two events that both must occur.
10、A joint probability of A and B must always be:
A) less than or equal to the conditional probability of A given B.
B) greater than or equal to the conditional probability of A given B.
C) greater than or equal to than the probability of A or B.
D) less than the probability of A and the probability of B.
The correct answer was A)
By the formula for joint probability: P(AB)=P(A| B) x P(B), since P(B) ≤ 1, then P(AB) ≤P(A|B). None of the other choices must hold.
11、A very large company has equal amounts of male and female employees. If a random sample of four employees is selected, what is the probability that all four employees selected are female?
A) 0.0625.
B) 0.0256
C) 0.1600
D) 1.0000
The correct answer was A)
Each employee has equal chance of being male or female. Hence, probability of 4 “successes” = (0.5)4 = 0.0625
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