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(a) I can choose 'a', 'b' or 'c'. If I choose 'b' then I get $200. If I choose 'c' then one of three things could happen: I could get $160 with probability 0.3; $400 with probability 0.1; or $80 with probability 0.6. If I choose 'a' then I enter a lottery where two possible outcomes could occur: with probability 0.6 I would collect $150; and with probability 0.4 I can choose either 'd’ with a return of $240 or 'e' which results in $1000 with a probability of 0.2 or $100 with a probability of 0.8. (b) I can choose either 'A' or 'B'. If I choose A', I get either $50 with probability 0.3 or, with probability 0.7, I get a choice between C' and 'D' (i.e. a decision node). If I choose C' I then get an equal chance of getting $20 or $80. If I choose 'D' I get $60 with probability 0.6 or $40 with probability 0.4. If I choose B' I get $60 with probability 0.8 or else a choice between 'E' and F'. If I choose 'E' I get $70 with probability 0.6 or $50 with probability 0.4. If I choose 'F' I get $500 with probability 0.1 or $10 with probability 0.9.

(a) I can choose 'a', 'b' or 'c'. If I choose 'b' then I get $200. If I choose 'c' then one of three things could happen: I could get $160 with probability 0.3; $400 with probability 0.1; or $80 with probability 0.6. If I choose 'a' then I enter a lottery where two possible outcomes could occur: with probability 0.6 I would collect $150; and with probability 0.4 I can choose either 'd’ with a return of $240 or 'e' which results in $1000 with a probability of 0.2 or $100 with a probability of 0.8. (b) I can choose either 'A' or 'B'. If I choose A', I get either $50 with probability 0.3 or, with probability 0.7, I get a choice between C' and 'D' (i.e. a decision node). If I choose C' I then get an equal chance of getting $20 or $80. If I choose 'D' I get $60 with probability 0.6 or $40 with probability 0.4. If I choose B' I get $60 with probability 0.8 or else a choice between 'E' and F'. If I choose 'E' I get $70 with probability 0.6 or $50 with probability 0.4. If I choose 'F' I get $500 with probability 0.1 or $10 with probability 0.9.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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3 Decision trees. Draw the decision trees that correspond to the following descriptions. What is the EMV of each of the trees? (a) I can choose 'a', 'b' or 'c'. If I choose 'b' then I get $200. If I choose 'c' then one of three things could happen: I could get $160 with probability 0.3; $400 with probability 0.1; or $80 with probability 0.6. If I choose 'a' then I enter a lottery where two possible outcomes could occur: with probability 0.6 I would collect $150; and with probability 0.4 I can choose either 'd' with a return of $240 or 'e' which results in $1000 with a probability of 0.2 or $100 with a probability of 0.8. (b) I can choose either 'A' or 'B'. If I choose A', I get either $50 with probability 0.3 or, with probability 0.7, I get a choice between 'C' and 'D' (i.e. a decision node). If I choose C' I then get an equal chance of getting $20 or $80. If I choose 'D' I get $60 with probability 0.6 or $40 with probability 0.4. If I choose 'B' I get $60 with probability 0.8 or else a choice between 'E' and F'. If I choose 'E' I get $70 with probability 0.6 or $50 with probability 0.4. If I choose 'F' I get $500 with probability 0.1 or $10 with probability 0.9.
Transcribed Image Text:3 Decision trees. Draw the decision trees that correspond to the following descriptions. What is the EMV of each of the trees? (a) I can choose 'a', 'b' or 'c'. If I choose 'b' then I get $200. If I choose 'c' then one of three things could happen: I could get $160 with probability 0.3; $400 with probability 0.1; or $80 with probability 0.6. If I choose 'a' then I enter a lottery where two possible outcomes could occur: with probability 0.6 I would collect $150; and with probability 0.4 I can choose either 'd' with a return of $240 or 'e' which results in $1000 with a probability of 0.2 or $100 with a probability of 0.8. (b) I can choose either 'A' or 'B'. If I choose A', I get either $50 with probability 0.3 or, with probability 0.7, I get a choice between 'C' and 'D' (i.e. a decision node). If I choose C' I then get an equal chance of getting $20 or $80. If I choose 'D' I get $60 with probability 0.6 or $40 with probability 0.4. If I choose 'B' I get $60 with probability 0.8 or else a choice between 'E' and F'. If I choose 'E' I get $70 with probability 0.6 or $50 with probability 0.4. If I choose 'F' I get $500 with probability 0.1 or $10 with probability 0.9.
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