Probability Questions

The correlation of returns between Stocks A and B is 0.50. The covariance between these two securities is 0.0043, and the standard deviation of the return of Stock B is 26%. The variance of returns for Stock A is:A. 0.0011.B. 0.0331.C. 0.2656.

There are ten sprinters in the finals of a race. How many different ways can the gold, silver, and bronze medals be awarded?A. 120.B. 720.C. 1,440.

Two events are said to be independent if the occurrence of one event:A. means that the second event cannot occur.B. means that the second event is certain to occur.C. does not affect the probability of the occurrence of the other event.

Jay Hamilton, CFA, is analyzing Madison, Inc., a distressed firm. Hamilton believes the firm's survival over the next year depends on the state of the economy. Hamilton assigns probabilities to four economic growth scenarios and estimates the probability of bankruptcy for Madison under each: Prob of growth Prob of bankruptcyRecession (< 0%) 20% 60%Slow growth (0% to 2%) 30% 40%Normal growth (2% to 4%) 40% 20%Rapid growth (> 4%) 10% 10%Based on Hamilton's estimates, the probability that Madison, Inc. does not go bankrupt in the next year is closest to:A) 67%.B) 18%.C) 33%.

Two mutually exclusive events:A. always occur together.B. cannot occur together.C. can sometimes occur together.

The probability that the DJIA will increase tomorrow is 2/3. The probability of an increase in the DJIA stated as odds is:A. two-to-one.B. one-to-three.C. two-to-three.

Among 900 taxpayers with incomes below $100,000, 35 were audited by the IRS. The probability that a randomly chosen individual with an income below $100,000 was audited is closest to:A. 0.039.B. 0.125.C. 0.350.

Assume two stocks are perfectly negatively correlated. Stock A has a standard deviation of 10.2% and stock B has a standard deviation of 13.9%. What is the standard deviation of the portfolio if 75% is invested in A and 25% in B?A) 0.00%.B) 4.18%.C) 0.17%.

Given the conditional probabilities in the table below and the unconditional probabilities P(Y = 1) = 0.3 and P(Y = 2) = 0.7, what is the expected value of X?xi P(xi\Y= 1) P(xi \ Y= 2)0 0.2 0.15 0.4 0.8A. 5.0B. 5.3C. 5.7

At a charity ball, 800 names are put into a hat. Four of the names are identical. On a random draw, what is the probability that one of these four names will be drawn?A. 0.004.B. 0.005.C. 0.010.

There is a 30% chance that the economy will be good and a 70% chance that it will be bad. If the economy is good, your returns will be 20% and if the economy is bad, your returns will be 10%. What is your expected return?A) 13%.B) 17%.C) 15%.

There is an 80% chance that the economy will be good next year and a 20% chance that it will be bad. If the economy is good, there is a 60% chance that XYZ Incorporated will have EPS of $3.00 and a 40% chance that their earnings will be $2.50. If the economy is bad, there is a 70% chance that XYZ Incorporated will have EPS of $1.50 and a 30% chance that their earnings will be $1.00. What is the firm's expected EPS?A) $2.00.B) $4.16.C) $2.51.

If a firm is going to create three teams of four from twelve employees. Which approach is the most appropriate for determining how the twelve employees can be selected for the three teams?A) Permutation formula.B) Labeling formula.C) Combination formula.

For assets A and B we know the following: E(RA) = 0.10, E(RB) = 0.20, Var(RA) = 0.25, Var(RB) = 0.36 and the correlation of the returns is 0.6. What is the expected return of a portfolio that is equally invested in the two assets?A) 0.3050.B) 0.2275.C) 0.1500.

A conditional expectation involves:A) refining a forecast because of the occurrence of some other event.B) calculating the conditional variance.C) determining the expected joint probability.

Compute the standard deviation of a two-stock portfolio if stock A (40% weight) has a variance of 0.0015, stock B (60% weight) has a variance of 0.0021, and the correlation coefficient for the two stocks is -0.35?A) 1.39%.B) 2.64%.C) 0.07%.

Which of the following statements about counting methods is least accurate?A) The labeling formula determines the number of different ways to assign a given number of different labels to a set of objects.B) The multiplication rule of counting is used to determine the number of different ways to choose one object from each of two or more groups.C) The combination formula determines the number of different ways a group of objects can be drawn in a specific order from a larger sized group of objects.

A two-sided but very thick coin is expected to land on its edge twice out of every 100 flips. And the probability of face up (heads) and the probability of face down (tails) are equal. When the coin is flipped, the prize is $1 for heads, $2 for tails, and $50 when the coin lands on its edge. What is the expected value of the prize on a single coin toss?A) $1.50.B) $2.47.C) $17.67.

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, but not both?A) 7.7%.B) 10.5%.C) 64.2%.

The covariance of returns on two investments over a 10-year period is 0.009. If the variance of returns for investment A is 0.020 and the variance of returns for investment B is 0.033, what is the correlation coefficient for the returns?A) 0.350.B) 0.444.C) 0.687.