Module 1 Assignment (MBA 550 Decisions Support Systems)

P(I|S) = 0.18, P(I|NS) = 0.06.

You are required to calculate P(S/I). Just try to relate this to the Bayesian formula under Bayesian Analysis section in the textbook.

Hint: you may relate smokers and non-smokers to Olson and Abercrombie respectively, and winning to illness in the attached sample solution for EXC #11.

Exercise # 12 and #14 – These exercises are very similar to Figure 7 (for part a of #14) and Table 1 (for part b of #14) shown in the section: Depending Events in the textbook. You can use these as a guide for layout. You are given marginal probabilities and conditional probabilities in both exercises. From this data calculate joint probabilities. Read the problem and identify marginal probability P(B) and conditional probability P(A|B) for each event, then multiply them together to calculate the joint probability using the following equation:

P(AB) = P(A|B) * P(B)

In exercise #12 you are given the marginal probability of Democrats P(D) = 0.66 and marginal probability of Republicans P(R) = 0.34 in the Senate. Start probability tree with these marginal probabilities. You are also given the conditional probabilities whether they will vote in favor or against the bill depending on the party they belong. For example, you are given that 35% of democrats’ favor (this also mean 65% do not favor the bill). This is called conditional probability P(F|D) since 35% senators who favor the bill belong to the Democratic party. You are also given the conditional probability of Republicans who favor/against the bill.

Use part a and b of the sample solution file for exercise #11 to solve this problem. Calculate the joint probability who favors the bill from both parties (similar to cell B41 in the sample solution, where I have calculated the total joint probability of winning the case by both firms). For simple majority if it is 50% or higher then the bill will pass.

In exercise # 14 you are given three marginal probabilities of students living in each district (North, South, and Central). These are 25%, 40% and 35% in the North, Central, and South districts respectively. You are also given the conditional probabilities of failing and passing (passing = 1-failing) in each region. For example, conditional probability of students who failed the test from North district P(F|N) = 0.1 or 10%. From this information you can also compute the conditional probability of students who passed from the North district is 90% (100-10) or 0.9. You are given similar data for other two districts.

For the H/W exercises in chapter 11, important thing is to determine the marginal and conditional probabilities. As you can see from the example in the Dependent Events section, the marginal probabilities are the probabilities of getting a head P(H) or a tail P(T) by tossing a coin. These probabilities are used to draw the probability tree in figure 7. Since the probability of drawing a red or white ball depends whether you got head or tail when the coin was tossed, so these are called conditional probabilities and are written as P(R|H), P(R|T) etc.

How to draw arrows? Word and Excel have a drawing button under the INSERT tab. In Excel, to draw arrows for the probability tree, click on Insert tab, then in the Illustrations group click on (drop-down arrow) of Shapes You can select number of shapes including arrows.

.Final Note: This course is numerical in nature. Since H/W is part of the overall grade, please do not ask me to check your answer/s prior to submitting the H/W. I do not provide feedback before the final submission and grading. However, if you have question/s regarding the material you have read; sample solution files I have supplied; examples in the textbook; or exercises at the back of each chapter that are not part of the graded H/W, please let me know. I will be happy to help.

Have a great week

Dr. Bal

Dr. B. Bal Page 3