Assume that you are planning to have a party at your house. Youreally would like to have the party outside in the sun, but thereis a chance that it might rain. You have two decisions to make –whether or not you will watch the forecast and then whether to havethe party inside or outside. If you choose to watch the forecast,it will either tell you that the weather will be sunny or that itwill be rainy. If you choose to watch the forecast, you will nothave to make the location decision until after you see theforecast. If you do not watch the forecast, you do not get to knowwhat the forecast would have said had you watched it – you need tomake the location decision without the knowledge of the forecast.However, the forecast is imperfect (probabilities are below). Italso costs you some time, and you are already cutting it close interms of getting ready.

Your task is to draw the decision tree for this situation,answer some questions about the decision tree, and recommend acourse of action on the basis if your analysis.

The information you will need:

Probabilities (note that p(A|B) signifies the probability ofevent A given that event B has occurred – it is a conditionalprobability).

p(forecast says it will be sunny) = 0.95

p(it is sunny|forecast said it would be sunny) = 0.99

p(it is sunny|forecast said it would be rainy) = 0.15

p(sunny) = 0.948 [hint: this is to use on the branch of the treewhere you decide not to watch the forecast]

Utilities (note that U(case X) represents the utility of caseX)

U(watch forecast, party indoors, sunny weather) = 0.3

U(watch forecast, party indoors, rainy weather) = 0.4

U(watch forecast, outdoors, sunny weather) = 0.9

U(watch forecast, outdoors, rainy weather) = 0.0

U(do not watch forecast, indoors, sunny weather) = 0.4

U(do not watch forecast, indoors, rainy weather) = 0.5

U(do not watch forecast, outdoors, sunny weather) = 1.0

U(do not watch forecast, outdoors, rainy weather) = 0.1

(a) (10 points): Draw the decision tree for this problem.Include clear labels for all branches. Include all probabilitiesand utilities.

(b) (10 points): If you choose to watch the forecast and it saysthat the weather will be sunny, should you have the party indoorsor outdoors? What is your expected utility for this choice?

(c) (5 points): What should your sequence of decisions be? Inother words, should you watch the forecast? If you do watch theforecast, what is the optimal location decision for each of the twopossible forecast reports? What is your expected utility for theoverall decision situation?

d) (10 points): Analyzing a simple party problem might seemsilly. However, the structure of this tree has many importantapplications in engineering. Think of a project managementsituation that could be described by this structure of decisiontree. Write a one-paragraph description of the decision situationyou think of (like the description at the beginning of thisquestion), and re-draw the tree with new labels on the branches.You do not need to include any probabilities or utilities on yournew tree.