Note: In addition to True/False and numerical questions, this homework will ask you to practice drawing two decision trees. The trees you draw will not be graded as the correct trees are provided in this document. However, it is important that you compare your tree to the answers and ensure that you can draw a decision tree based on a problem description. This skill is essential to do well in the next module and the exams.
Why do we care about the shape of the nodes? If you use a wrong shape, then it is easy to get confused between a decision and an uncertain event, especially for a complex decision tree. A decision is something you have control over (you make the choice; you choose which option/alternative you want). An uncertain event is something you don't have control over its outcome.
1. True of False.
a. We use a circle to represent a decision node.
b. A chance node links to several uncertain outcomes. We use a square to represent a chance node.
c. A decision tree may contain more than one decision node.
2. John's garage is considering hiring another mechanic. With an additional mechanic, if there are a lot of accidents in San Jose this year, then John anticipates making an additional $75,000 profit. However, if there are not a lot of accidents, then John's garage could lose $20,000 due to the salary/benefits for the additional mechanic. John thinks that there will be a 30% chance of " a lot of accidents" and a 70% chance of "not a lot of accidents". Assume if John's garage doesn't expand, then he will have the same profit as last year.
a. Draw a decision tree for John. (Draw the tree on your own first, then check the answer on the next page.)
b. What is the expected change in profit (could be a gain or a loss) if John's garage decides to hire another mechanic. [If the expected change in profit is negative, don't forget to include the negative sign in your answer.]
c. Tell John what he should do (use the expected value criterion). A) Hire an additional mechanic.B) Do not hire an additional mechanic.
C) There is not enough information to reach a conclusion.
3. Your regular tennis partner has made a friendly wager with you. The two of you will play out one point in which you can serve. The loser pays the winner $100. If your first serve is not in play, you get a second serve. If your second serve is not in play, you lose the point. You have two kinds of serves: a hard one and a soft one. You know that your hard serve is in play 65% of the time and, when it is in play, you win the point 75% of the time. You put your soft serve in play 80% of the time, and when it is in play, you win the point 50% of the time. [Note: You will need a second serve only if your first serve is not in play. You may use different types of serves in two serves.]
a. Draw a decision tree for this problem. [Draw a tree on your own before checking the answer on the next page.]
b. Calculate the expected point for each possible strategy. Use expected point as your decision criterion. Should you accept the wager? If so, what is your strategy? (Choose the best answer.)
A) Do not accept the wager.
B) Accept the wager. Use hard serve all the way.
C) Accept the wager. Use soft serve all the way.
D) Accept the wager. Use hard serve first. If the first serve is not in play, then use soft serve.
E) Accept the wager. Use soft serve first. If the first serve is not in play, then then use soft serve.
Attachment:- images.rar