Probability Questions

For the task of arranging a given number of items without any sub-groups, this would require:A) the labeling formula.B) only the factorial function.C) the permutation formula.

The covariance of the returns on investments X and Y is 18.17. The standard deviation of returns on X is 7%, and the standard deviation of returns on Y is 4%. What is the value of the correlation coefficient for returns on investments X and Y?A) +0.85.B) +0.65.C) +0.32.

An analyst announces that an increase in the discount rate next quarter will double her earnings forecast for a firm. This is an example of a:A) conditional expectation.B) use of Bayes' formula.C) joint probability.

After repeated experiments, the average of the outcomes should converge to:A) the expected value.B) the variance.C) one.

There is a 90% chance that the economy will be good next year and a 10% chance that it will be bad. If the economy is good, there is a 60% chance that XYZ Incorporated will have EPS of $4.00 and a 40% chance that their earnings will be $3.00. If the economy is bad, there is an 80% chance that XYZ Incorporated will have EPS of $2.00 and a 20% chance that their earnings will be $1.00. What is the firm's expected EPS?A) $3.42.B) $5.40.C) $2.50.

For a given corporation, which of the following is an example of a conditional probability? The probability the corporation's:A) earnings increase and dividend increases.B) inventory improves.C) dividend increases given its earnings increase.

The following information is available concerning expected return and standard deviation of Pluto and Neptune Corporations:E(r) StdevPluto Corporation 11% 0.22Neptune Corporation 9% 0.13If the correlation between Pluto and Neptune is 0.25, determine the expected return and standard deviation of a portfolio that consists of 65% Pluto Corporation stock and 35% Neptune Corporation stock.A) 10.3% expected return and 16.05% standard deviation.B) 10.3% expected return and 2.58% standard deviation.C) 10.0% expected return and 16.05% standard deviation.

If given the standard deviations of the returns of two assets and the correlation between the two assets, which of the following would an analyst least likely be able to derive from these?A) Strength of the linear relationship between the two.B) Covariance between the returns.C) Expected returns.

For an unconditional probability:A) there are at least two events.B) there is only one random variable of concern.C) the addition rule is important.

Jessica Fassler, options trader, recently wrote two put options on two different underlying stocks (AlphaDog Software and OmegaWolf Publishing), both with a strike price of $11.50. The probabilities that the prices of AlphaDog and OmegaWolf stock will decline below the strike price are 65% and 47%, respectively. The probability that at least one of the put options will fall below the strike price is approximately:A) 0.31.B) 1.00.C) 0.81.

The returns on assets C and D are strongly correlated with a correlation coefficient of 0.80. The variance of returns on C is 0.0009, and the variance of returns on D is 0.0036. What is the covariance of returns on C and D?A) 0.40110.B) 0.00144.C) 0.03020.

Data shows that 75 out of 100 tourists who visit New York City visit the Empire State Building. It rains or snows in New York City one day in five. What is the joint probability that a randomly choosen tourist visits the Empire State Building on a day when it neither rains nor snows?A) 95%.B) 60%.C) 15%.

Helen Pedersen has all her money invested in either of two mutual funds (A and B). She knows that there is a 40% probability that fund A will rise in price and a 60% chance that fund B will rise in price if fund A rises in price. What is the probability that both fund A and fund B will rise in price?A) 1.00.B) 0.40.C) 0.24.

The multiplication rule of probability is used to calculate the:A) probability of at least one of two events.B) unconditional probability of an event, given conditional probabilities.C) joint probability of two events.

In a given portfolio, half of the stocks have a beta greater than one. Of those with a beta greater than one, a third are in a computer-related business. What is the probability of a randomly drawn stock from the portfolio having both a beta greater than one and being in a computer-related business?A) 0.667.B) 0.333.C) 0.167.

A firm holds two $50 million bonds with call dates this week.The probability that Bond A will be called is 0.80.The probability that Bond B will be called is 0.30.The probability that at least one of the bonds will be called is closest to:A) 0.86.B) 0.24.C) 0.50.

The probability of a new Wal-Mart being built in town is 64%. If Wal-Mart comes to town, the probability of a new Wendy's restaurant being built is 90%. What is the probability of a new Wal-Mart and a new Wendy's restaurant being built?A) 0.576.B) 0.675.C) 0.306.

There is a 50% chance that the Fed will cut interest rates tomorrow. On any given day, there is a 67% chance the DJIA will increase. On days the Fed cuts interest rates, the probability the DJIA will go up is 90%. What is the probability that tomorrow the Fed will cut interest rates or the DJIA will go up?A) 0.33.B) 0.72.C) 0.95.

Which of the following is an a priori probability?A) For a stock, based on prior patterns of up and down days, the probability of the stock having a down day tomorrow.B) The probability the Fed will lower interest rates prior to the end of the year.C) On a random draw, the probability of choosing a stock of a particular industry from the S& 500.

Each lottery ticket discloses the odds of winning. These odds are based on:A) past lottery history.B) the best estimate of the Department of Gaming.C) a priori probability.