1. The ________________________ of two events A and B is the event that consists of all the elements contained in A and B.
2. If A and B are mutually exclusive then A∩B = _________ and P(A∩B) = ________.
3. If A and B are independent, P(A∩B) = ____________________ (finish the formula).

4.  The law of large numbers says that if an experiment is repeated again and again, the         relative frequency probability will get closer to the _____________________________

5.  If the P(A\B) = 0.6 and P(A∩B) = 0.3, find P(B).

6.  If you roll a single fair die and count the number of dots on top, what is the probability of getting a number of at most 3 on a single throw?

7.  You roll two fair dice, a blue one and a yellow one. Each part has single probability.

1. Find P(odd number on the blue die and even on the yellow die).

     b)  Find P(even on the blue die and greater than 1 on the yellow die).

8.  An urn contains 12 balls identical in every respect except color.  There are 6 red balls, 4 green balls, and 2 blue balls. Each part has single probability.

     a)  You draw two balls from the urn, but replace the first ball before drawing the second.  Find the probability that the first ball is red and the second is green.

     b)  Repeat part (a), but do not replace the first ball before drawing the second.

9.  A computer package sale comes with four different choices of printers and five choices of monitors.  If a store wants to display each package combination that is for sale, how many packages must be displayed?   

10.  You have 100 parts in a box and 25 of them are bad.  What is the probability that:

            a)         the first part you draw will be bad?

            b)         the first part will be good?

            c)         if you draw two parts, both will be good?

2) When the real wage is above the level that equilibrates supply and demand:

Select one:

a. It creates a deadweight loss in the labor market.

b. the quantity of labor demanded exceeds the quantity supplied.

c. GDP definitely rises.

d. Interest rate rises.

3) If Central Bank A cares only about keeping the price level stable and Central Bank B cares only about keeping output at its natural level, then in response to an exogenous increase in the price of oil:

Select one:

a. both Central Bank A and Central Bank B should increase the quantity of money.

b. Central Bank A should increase the quantity of money, whereas Central Bank B should keep it stable.

c. Central Bank A should decrease the quantity of money, whereas Central Bank B should increase it.

d. both Central Bank A and Central Bank B should keep the quantity of money stable.

4) In a Keynesian Cross economy without the foreign sector, the marginal propensity to save is 0.2. Investment is 100; government expenditure is also 100. Taxes are 100. How much does total savings change if marginal propensity to save goes up from 0.2 to 0.3?

a. goes up by 90

b. goes up by 100

c. does not change

d. None of the above or cannot be determined without more information

5) Using the simple Keynesian Cross analysis, assume that the consumption function is given by C = 100 + 0.6(Y-T). If planned investment is 200 and T is 300, the level of G needed to make equilibrium Y equal 1,000 is (assume that net exports are zero):

Select one:

a. 60

b. 240

c. 250

d. 280

e. None of the above.

In 2018 in an attempt to improve the reputation of the Democratic People’s Republic of Korea (DPRK) lottery tickets were sold to people around the world. The grand prize of this lottery was a weekend with Kim Jung Un. During anevening with Kim Jung Un the lottery winner was offered a meal made from one of the lobsters in Kim Jung Un’s private lobster aquarium.(Which by the way are all Maine lobsters!) The average weight of the lobsters was 22 ounces and the standard deviation was 0.67 ounces. When a random lobster wastaken from Kim Jung Un’s aquarium what was the probability it weighed more than 23.75 ounces?
a.) 0.0154 b.) 0.9955 c.) 0.9846 d.) 0.0045 e.)None of these

In lieu of using a single resistor three resistors are wired in series. The three resistors are identical. The resistance o f each is normally distributed with a mean of 6 ohms and a standard deviation of 0.3 ohms. The probability the combined resistance will exceed 19 ohm's is 0.0274. How precise (i.e. what is the required value of the standard deviation) would the manufacturing process have to be make the probability less than 0.0055 that t he combined resistance of the circuit would exceed 19 ohms?
a.) 0.180 ohms b.) 0.220 ohms c.) 0.227 ohms d.) 0.229 ohms e.) None of these

An experiment has two possible outcomes: the first occurs with probability p ; the second with probability p^2 . What is p?
a.) 0.3820 b.) 0.5000    c.) 0.2500     d.)   0.6180 e.) None of the above

Of all 3–to–5year old children, 56% are enrolled in school. If a sample of 500 such children is randomly selected, find the probability that at least 250 will be enrolled in school.Hint: Use De Moivre–Laplace.
a.) 0.9970 b.) 0.0035 c.) 0.9965 d.) 0.0030 e.) None of the above

Hartman Company is trying to determine how much of each of two products should be produced over the coming planning period. The only serious constraints involve labor availability in three departments. Shown below is information concerning labor availability, labor utilization, overtime, and product profitability.

If all production is done in a standard workweek, then Profit per Unit includes the cost to pay for the workforce. But, if overtime is needed in each department, then the Profit Function needs to be reduced by the Cost per Hour of Overtime in Each Department multiplied by the Number of Overtime Hours Used in Each Department. For example, if we used 5 hours of Overtime in Department A, we would need to Subtract $15*5 from our Profit equation.


Setup and Solve the Linear Programming Problem and determine the number of units of Product 1 and Product 2 to produce to Maximize Profit. Add an Additional Constraint to your LP to make sure that ALL of the Variables are INTEGERS


Hint: You will need 5 Decision Variables, 2 of them to determine the production quantities, and 3 of them to determine how much overtime to use in each of the departments.


Max Profit = $

(Do Not Use Commas) Hint: Max Profit is Between $3328 and $3578
Number of Units of Product 1 to Produce =

Number of Units of Product 2 to Produce =

Overtime in Department A =

hours
Overtime in Department B =

hours
Overtime in Department C =

hours

Layton Machining Company (LMC) manufactures two versions of a basic machine tool. One version is a standard model and one is a custom model, which requires some additional work and slightly higher-grade materials. The manufacturing process at LMC requires that each product go through two departments, Grinding and Finishing. The process in each department uses a single type of machine. Total machine capacity in Grinding is 51,000 hours, and in Finishing, total machine capacity is 31,000 hours. (Each department has multiple machines.) Total market demand is limited to 102,000 standard units and 122,000 custom units monthly. LMC is currently producing 92,000 standard units and 53,000 custom units each month. Cost and machine-usage data for the two products follow:

a. What is the optimal production schedule for LMC? In other words, how many standard units and custom units should the company produce each month to maximize monthly profit?

Standard Units ____

Custom Units ____

b. If LMC produces at the level found in requirement (a), how much will monthly profit increase over the current production schedule?

Increase profits by ____

Eliminating Entries, Previously Unreported Intangibles, Goodwill

Pirin Company acquires all of the voting stock of Skoda Automotive for $40 million in cash. Skoda’s balance sheet accounts at the date of acquisition are listed below.

Date-of-acquisition book values approximate fair value for all reported assets and liabilities. The following previously unreported intangibles are identified as belonging to Skoda, along with their estimated fair values at the date of acquisition (in millions):

Required

a. Prepare a schedule calculating the goodwill to be recognized for this acquisition.

Do not use negative signs with your answers.

Enter answers in millions (do not round answers).

b. Prepare the eliminating entries necessary to consolidate the balance sheet accounts of Pirin and Skoda at the date of acquisition.  

Enter answers in millions. Do not round answers.

Investment companies and performance evaluation

1) Consider two different hedge funds with the following data related to performance:

Hedge fund Alpha Beta

Fund A   5% 1.6

Fund B   3% 0.8

Assuming that beta is consistent with the type of investing we expected in both cases, which fund performed better.
A. Fund A, because it had the higher return
B. Fund A, because it had the higher alpha
C. Fund B, because its alpha is more impressive than Fund A when we consider how much less risk the fund took.
D. Fund B, because the beta is closer to 1.

2) When we analyze the performance of an actively managed mutual fund we find that the fund generated a beta of 1 and an alpha of zero.

A. this result shows that the manager took no risk when investing

B. this result shows that the manager did not add any value to performance with his/her decision-making

C. both (A) and (B) are true

D. none of the above

3) Consider two different hedge funds with the following data related to performance:

Hedge fund Alpha Beta

Fund A   1% 0.8

Fund B   3% -0.3
Assuming that beta is consistent with the type of investing we expected in both cases, which fund performed better?

A. Fund A, because Fund B should have negative alpha to match its negative beta
B. Fund A, because it had a higher beta than Fund B
C. Fund B, because its alpha is higher than Fund A.
D. Fund A, because the beta is closer to 1.

4) A positive alpha for a mutual fund means:

A. the fund invested in high-risk strategies

B. the fund manager’s performance was bad

C. both (A) and (B)

D. none of the above

Question 6 options:

Hartman Company is trying to determine how much of each of two products should be produced over the coming planning period. The only serious constraints involve labor availability in three departments. Shown below is information concerning labor availability, labor utilization, overtime, and product profitability.

If all production is done in a standard workweek, then Profit per Unit includes the cost to pay for the workforce. But, if overtime is needed in each department, then the Profit Function needs to be reduced by the Cost per Hour of Overtime in Each Department multiplied by the Number of Overtime Hours Used in Each Department. For example, if we used 5 hours of Overtime in Department A, we would need to Subtract $13*5 from our Profit equation.


Setup and Solve the Linear Programming Problem and determine the number of units of Product 1 and Product 2 to produce to Maximize Profit. Add an Additional Constraint to your LP to make sure that ALL of the Variables are INTEGERS


Hint: You will need 5 Decision Variables, 2 of them to determine the production quantities, and 3 of them to determine how much overtime to use in each of the departments.


Max Profit = $

(Do Not Use Commas) Hint: Max Profit is Between $3393 and $3743
Number of Units of Product 1 to Produce =

Number of Units of Product 2 to Produce =

Overtime in Department A =

hours
Overtime in Department B =

hours
Overtime in Department C =

hours

Problem 13-09 (Algorithmic)

Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):

1. What is the decision to be made, what is the chance event, and what is the consequence for this problem?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
   How many decision alternatives are there?
   
   Number of decision alternatives =
   
   How many outcomes are there for the chance event?
   
   Number of outcomes =
   
2. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative and minimax regret approaches?
   

   Optimistic approach
   Conservative approach
   Minimax regret approach

3. Suppose that management of Myrtle Air Express believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach to determine an optimal decision.
   
   Optimal Decision :  
   
4. Suppose that the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What is the optimal decision using the expected value approach?
   
   Optimal Decision :  
   
5. Determine the range of demand probabilities for which each of the decision alternatives has the largest expected value. If required, round your answer to four decimal places.
   
     is the best choice if probability of strong demand is less than or equal to . For values of  greater than , the full price service is   choice.