The following is a modification of one of the examples presented in class. There are two candidate cars Cl and C2. Each can either be of good quality or badquality. There are two possible tests. Tl on Cl costs $100. T2 on C2 costs $50. Cl costs $1500, which is $500 below market value. If Cl is of bad quality, the repair cost is $700 C2 costs $1150, which is $250 below market value. If C2 is of bad quality, the repair costs $150. The chance that car Cl is of good quality is 70%. The chance that car C2 is of good quality is 80%. Test TI on Cl will confirm good quality with probability 80% and bad quality with probability 65%. Test T2 on C2 will confirm good quality with probability 75% and bad quality with probability 70%. The buyer must buy one of the two cars and can perform TI, T2, T1 and T2 simultaneously, T1 followed by T2, or T2 followed by T1. The total cost of performing the two tests simultaneously is $125 (this includes the cost of the T1 and T2) and the total cost of performing one test followed by the other is $175 (again including the cost of performing T1 and T2). 1) Build a decision tree for this problem. Only draw the branch that corresponds to T1 being performed first. Note: You do not have to repeatedly draw similar branches. Just draw a representative branch and explain what the other branches might be that you did not end up drawing.

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The following is a modification of one of the examples presented in class.
There are two candidate cars Cl and C2. Each can either be of good quality or badquality.
There are two possible tests. T1 on Cl costs $100. T2 on C2 costs $50.
Cl costs $1500, which is $500 below market value. If Cl is of bad quality, the repair cost is $700
C2 costs $1150, which is $250 below market value. If C2 is of bad quality, the repair costs $150.
The chance that car Cl is of good quality is 70%.
The chance that car C2 is of good quality is 80%.
Test T1 on C1 will confirm good quality with probability 80% and bad quality with probability 65%.
Test T2 on C2 will confirm good quality with probability 75% and bad quality with probability 70%.
The buyer must buy one of the two cars and can perform Tl, T2, T1 and T2 simultaneously, T1 followed by T2,
or T2 followed by T1. The total cost of performing the two tests simultaneously is $125 (this includes the cost of
the T1 and T2) and the total cost of performing one test followed by the other is $175 (again including the cost of
performing T1 and T2).
1) Build a decision tree for this problem. Only draw the branch that corresponds to T1 being performed first.
Note: You do not have to repeatedly draw similar branches. Just draw a representative branch and explain what
the other branches might be that you did not end up drawing.
Transcribed Image Text:The following is a modification of one of the examples presented in class. There are two candidate cars Cl and C2. Each can either be of good quality or badquality. There are two possible tests. T1 on Cl costs $100. T2 on C2 costs $50. Cl costs $1500, which is $500 below market value. If Cl is of bad quality, the repair cost is $700 C2 costs $1150, which is $250 below market value. If C2 is of bad quality, the repair costs $150. The chance that car Cl is of good quality is 70%. The chance that car C2 is of good quality is 80%. Test T1 on C1 will confirm good quality with probability 80% and bad quality with probability 65%. Test T2 on C2 will confirm good quality with probability 75% and bad quality with probability 70%. The buyer must buy one of the two cars and can perform Tl, T2, T1 and T2 simultaneously, T1 followed by T2, or T2 followed by T1. The total cost of performing the two tests simultaneously is $125 (this includes the cost of the T1 and T2) and the total cost of performing one test followed by the other is $175 (again including the cost of performing T1 and T2). 1) Build a decision tree for this problem. Only draw the branch that corresponds to T1 being performed first. Note: You do not have to repeatedly draw similar branches. Just draw a representative branch and explain what the other branches might be that you did not end up drawing.
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