aianjie

 

9、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?

A) 64.2%.

B) 7.7%.

C) 10.5%.

D) 67.0%.

aianjie

 

The correct answer is B

Using the addition rule, the probability of being accepted at Harvard or Yale, is equal to: P(Harvard) + P(Yale) ? P(Harvard and Yale) = 0.25 + 0.42 ? 0.028 = 0.642 or 64.2%.

aianjie

 

10、A joint probability of A and B must always be:

A) greater than or equal to the conditional probability of A given B.

B) greater than or equal to than the probability of A or B.

C) less than or equal to the conditional probability of A given B.

D) less than the probability of A and the probability of B.

aianjie

 

The correct answer is C

By the formula for joint probability: P(AB)=P(A|B) × P(B), since P(B) ≤ 1, then P(AB) ≤P(A|B). None of the other choices must hold.

aianjie

 

11、A conditional expectation involves:

A) refining a forecast because of the occurrence of some other event.

B) determining the expected joint probability.

C) calculating the conditional variance.

D) estimating the skewness.

aianjie

 

The correct answer is A

Conditional expected values are contingent upon the occurrence of some other event. The expectation changes as new information is revealed.

aianjie

 

12、An investor has an A-rated bond, a BB-rated bond, and a CCC-rated bond where the probabilities of default over the next three years are 4 percent, 12 percent, and 30 percent, respectively. What is the probability that all of these bonds will default in the next three years if the individual default probabilities are independent?

A) 1.44%.

B) 23.00%.

C) 0.14%.

D) 46.00%.

aianjie

 

The correct answer is C

Since the probability of default for each bond is independent, P(ABBCCC) = P(A) × P(BB) × P(CCC) = 0.04 × 0.12 × 0.30 = 0.00144 = 0.14%.

aianjie

 

13、If a fair coin is tossed twice, what is the probability of obtaining heads both times?

A) 1/2.

B) 3/4. 

C) 1/4.

D) 1.

aianjie

 

The correct answer is C

The probability of tossing a head, H, is P(H) = 1/2. Since these are independent events, the probability of two heads in a row is P(HH) = P(H) × P(H) = 1/2 × 1/2 = 1/4.