1、Given the following table about employees of a company based on whether they are smokers or nonsmokers and whether or not they suffer from any allergies, what is the probability of suffering from allergies or being a smoker?

A)   0.88.

B)   0.12.

C)   0.38.

D)   0.20.

2、Given the following table about employees of a company based on whether they are smokers or nonsmokers and whether or not they suffer from any allergies, what is the probability of being either a nonsmoker or not suffering from allergies?

A)   0.38.

B)   0.88.

C)   0.50.

D)   1.50.

3、The following table summarizes the availability of trucks with air bags and bucket seats at a dealership.

What is the probability of selecting a truck at random that has either air bags or bucket seats?

A)   73 percent.

B)   34 percent.

C)   50 percent.

D)   107 percent.

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

A)   1.00.

B)   0.72.

C)   0.33.

D)   0.95.

5、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)   0.30.

D)   0.55.

答案和详解如下：

1、Given the following table about employees of a company based on whether they are smokers or nonsmokers and whether or not they suffer from any allergies, what is the probability of suffering from allergies or being a smoker?

	Suffer from Allergies	Don't Suffer from Allergies	Total
Smoker	35	25	60
Nonsmoker	55	185	240
Total	90	210	300

A)   0.88.

B)   0.12.

C)   0.38.

D)   0.20.

The correct answer was C)

The addition rule for probabilities is used to determine the probability of at least one event among two or more events occurring. The probability of each event is added and the joint probability (if the events are not mutually exclusive) is subtracted to arrive at the solution. P(smoker or allergies) = P(smoker) + P(allergies) – P(smoker and allergies) = (60/300) + (90/300) – (35/300) = 0.20 + 0.30 – 0.117 = 0.38.

Alternatively: 1 - Prob.(Neither) = 1 - (185/300) = 38.3%

2、Given the following table about employees of a company based on whether they are smokers or nonsmokers and whether or not they suffer from any allergies, what is the probability of being either a nonsmoker or not suffering from allergies?

	Suffer from Allergies	Don't Suffer from Allergies	Total
Smoker	35	25	60
Nonsmoker	55	185	240
Total	90	210	300

A)   0.38.

B)   0.88.

C)   0.50.

D)   1.50.

The correct answer was B)

The probability of being a nonsmoker is 240/300 = 0.80. The probability of not suffering from allergies is 210/300 = 0.70. The probability of being a nonsmoker and not suffering from allergies is 185/300 = 0.62. Since the question asks for the probability of being either a nonsmoker or not suffering from allergies we have to take the probability of being a nonsmoker plus the probability of not suffering from allergies and subtract the probability of being both: 0.80 + 0.70 - 0.62 = 0.88.

Alternatively: 1 - P(Smoker & Allergies) = 1 - (35/300) = 88.3%

3、The following table summarizes the availability of trucks with air bags and bucket seats at a dealership.

	Bucket Seats	No Bucket Seats	Total
Air Bags	75	50	125
No Air Bags	35	60	95
Total	110	110	220

What is the probability of selecting a truck at random that has either air bags or bucket seats?

A)   73 percent.

B)   34 percent.

C)   50 percent.

D)   107 percent.

The correct answer was A)

The addition rule for probabilities is used to determine the probability of at least one event among two or more events occurring. The probability of each event is added and the joint probability (if the events are not mutually exclusive) is subtracted to arrive at the solution. P(air bags or bucket seats) = P(air bags) + P(bucket seats) – P(air bags and bucket seats) = (125/220) + (110/220) – (75/220) = 0.57 + 0.50 – 0.34 = 0.73 or 73 percent.

Alternative: 1 - P(no airbag and no bucket seats) = 1 - (60/220) = 72.7%

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

A)   1.00.

B)   0.72.

C)   0.33.

D)   0.95.

The correct answer was B)    

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 x 0.90=0.45. Thus P (cut interest rates or DJIA increase) = 0.50 + 0.67 – 0.45 = 0.72.

5、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)   0.30.

D)   0.55.

The correct answer was 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.