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 Bfficeffice" />

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%.

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

aianjie

 

8、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) 0.70.

B) 0.80.

C) 0.60.

D) 0.85.

aianjie

 

The correct answer is B

P(AB) = P(A|B) × P(B)

0.68 / 0.85 = 0.80

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%.