## Calculate the probability that you will be able to keep a gum ball on the first try.

A paper bag contains a mixture of three types of candy. There are ten gum balls, seven candy bars, and three packages of toffee. Suppose a game is played in which a candy is randomly taken from the bag and then a second candy is drawn from the bag, without replacement. You are allowed to keep both candies, if, and only if, the second is the same type as the first.

a) Calculate the probability that you will be able to keep a gum ball on the first try.

b) Calculate the probability that you will be able to keep any candy on the first try.

c) Calculate the probability that you will not be able to keep any candy on the first try.

### Strategic Management Project

Assignment Content Review the Strategic Management Project Background and your strategic management research journal entries from Weeks 1–4. Create a 10-slide presentation for Caterpillar Inc. leadership in which you summarize your key findings, propose….

### Case Problem Investment Strategy

Case Problem Investment Strategy J. D. Williams, Inc. is an investment advisory firm that manages more than \$120 million in funds for its numerous clients. The company uses an asset allocation model that recommends the portion of each client’s portfolio to be invested in a growth stock fund, an income fund and a money market fund. To maintain diversity in each client’s portfolio, the firm places limits on the percentage of each portfolio that may be invested in each of the three funds. General guidelines indicate that the amount invested in the growth fund must be between 20% to 40% of the total portfolio value. Similar percentages for the other two funds stipulate that between 20% to 50% of the total portfolio must be in the income fund and at least 30% of the total portfolio value must be in the money market fund.   In addition, the company attempts to assess the risk tolerance of each client and adjust the portfolio to meet the needs of the individual investor. For example, Williams just contracted with a new client who has \$800,000 to invest. Based on an evaluation of the client’s risk tolerance, Williams assigned a maximum risk index of 0.05 for the client. The firm’s risk indicators show the risk of the growth fund at 0.10, the income fund at 0.07 and the money market fund at 0.01. An overall portfolio risk index is computed as a weighted average of the risk rating for the three funds where the weights are the fraction of the client’s portfolio invested in each of the funds. Additionally, William’s is currently forecasting annual yields of 18% for the growth fund, 12.5% for the income fund and 7.5% fir the money market fund. Based on the information provided, how should the new client be advised to allocate \$800,000 among the growth, income and money market funds? Develop a linear programming model that will provide the maximum yield for the portfolio. Use your model to develop a managerial report.   Managerial Report: a.Recommend how much of the \$800,000 should be invested in each of the three funds. What is the annual yield you anticipate for the investment recommendation change? b.Assume that the client’s risk index could be increased to 0.055. How much would the yield increase and how would the investment recommendation change? c.Refer again to the original situation where the client’s risk index was assessed to be 0.05. How would your investment recommendation change if the annual yield for the growth fund were revised downward to 16% or even to 14%? d.Assume that the client expressed some concern about having too much money in the growth fund. How would the original recommendation change if the amount invested in the growth fund is not allowed to exceed the amount invested in the income fund? e.The asset allocation model you developed may be useful in modifying the portfolios for all the firm’s clients whenever the anticipated yields for the three funds are periodically revised. What is your recommendation as to whether use of this model is possible?

### Case Analysis

You can view the article (the case), “The Man Who Got Honeywell’s Groove Backt”, by linking to the course EReserves  Follow the Case Analysis Outline given in your syllabus. This is….