答案和详解如下：

1、A very large company has twice as many male employees relative to 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)   0.0123.

C)   0.3333.

D)   0.6667.

The correct answer was B)

Since there are twice as many male employees to female employees, p(male) = 2/3 and p(female)=1/3. Therefore, the probability of 4 “successes” = (0.333)⁴ = 0.0123.

2、If two events are independent, the probability that they both will occur is:

A)   0.00.

B)   0.50.

C)   Cannot be determined from the information given.

D)   1.00.

The correct answer was C)

If two events are independent, their probability of their joint occurrence is computed as follows:  P(A∩B) = P(A) × P(B). Since we are not given any information on the respective probabilities of A or B, there is not enough information.

3、The probability of each of three independent events is shown in the table below. What is the probability of A and C occurring, but not B?

A)   3.8%.

B)   4.2%.

C)   10.5%.

D)   8.9%.

The correct answer was D)

Using the multiplication rule: (0.25)(0.42) – (0.25)(0.15)(0.42) = 0.08925 or 8.9%

4、If two fair coins are flipped and two fair six-sided dice are rolled, all at the same time, what is the probability of ending up with two heads (on the coins) and two sixes (on the dice)?

A)   0.4167.

B)   0.0039.

C)   0.0069.

D)   0.8333.

The correct answer was C)

For the four independent events defined here, the probability of the specified outcome is 0.5000 x 0.5000 x 0.1667 x 0.1667 = 0.0069.

5、A bond portfolio consists of four BB-rated bonds. Each has a probability of default of 24 percent and these probabilities are independent. What are the probabilities of all the bonds defaulting and the probability of all the bonds not defaulting?

A)         0.96000                      0.04000

B)         0.00332                      0.33360

C)         0.04000                0.96000

D)         0.06000                             0.19000

The correct answer was B)

For the four independent events where the probability is the same for each, the probability of all defaulting is (0.24)⁴. The probability of all not defaulting is (1-0.24)⁴.