3 Decision trees. Draw the decision trees that correspond to the following descriptions and then determine the EMV associated with each tree. (a) I can choose 'a' or 'b'. If I choose 'a' then I enter a lottery where two outcomes could occur: with probability 0.1 I would collect $80; and with probability 0.9 would lose $10 (i.e. collect -$10). If I choose ‘b’ then one of three things could happen: I could get Assignment 4 MATH 177, 2023 1 $20 with probability 0.2; lose $10 with probability 0.7; or enter into a bonus round with probability 0.1. In the bonus round I can choose options 'c' of 'd'. If I choose option 'c' then one of two things happen: I could get $200 with probability 0.05; or get $20 with probability 0.95. If I choose option 'd' I would collect $30. (b) I can choose either 'A' or 'B'. If I choose 'A', there is a 50% chance I get a choice between 'C' and 'D' (i.e. a decision node). If I choose 'C' I get $400 with probability 0.6 or $800 with probability 0.4. If I choose 'D' I then get $500. If I choose 'A' but did not get to choose between 'C' and 'D' then I instead get a choice between 'E' and 'F'. If I choose 'E' I get $300 with probability 0.7 or $1000 with probability 0.3. If I choose 'F' I then get $600. If I choose 'B' I get $400 with probability 0.8 or a choice between 'G' and 'H'. If I choose 'G' I get an equal chance of getting $200 or $700. If I choose 'H' I get $1200 with probability 0.4 or $0 with probability 0.6.
3 Decision trees. Draw the decision trees that correspond to the following descriptions and then determine the EMV associated with each tree. (a) I can choose 'a' or 'b'. If I choose 'a' then I enter a lottery where two outcomes could occur: with probability 0.1 I would collect $80; and with probability 0.9 would lose $10 (i.e. collect -$10). If I choose ‘b’ then one of three things could happen: I could get Assignment 4 MATH 177, 2023 1 $20 with probability 0.2; lose $10 with probability 0.7; or enter into a bonus round with probability 0.1. In the bonus round I can choose options 'c' of 'd'. If I choose option 'c' then one of two things happen: I could get $200 with probability 0.05; or get $20 with probability 0.95. If I choose option 'd' I would collect $30. (b) I can choose either 'A' or 'B'. If I choose 'A', there is a 50% chance I get a choice between 'C' and 'D' (i.e. a decision node). If I choose 'C' I get $400 with probability 0.6 or $800 with probability 0.4. If I choose 'D' I then get $500. If I choose 'A' but did not get to choose between 'C' and 'D' then I instead get a choice between 'E' and 'F'. If I choose 'E' I get $300 with probability 0.7 or $1000 with probability 0.3. If I choose 'F' I then get $600. If I choose 'B' I get $400 with probability 0.8 or a choice between 'G' and 'H'. If I choose 'G' I get an equal chance of getting $200 or $700. If I choose 'H' I get $1200 with probability 0.4 or $0 with probability 0.6.
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Transcribed Image Text:3 Decision trees. Draw the decision trees that correspond to the following descriptions and
then determine the EMV associated with each tree.
(a) I can choose 'a' or 'b'. If I choose 'a' then I enter a lottery where two outcomes could
occur: with probability 0.1 I would collect $80; and with probability 0.9 would lose $10
(i.e. collect -$10). If I choose ‘b’ then one of three things could happen: I could get
Assignment 4
MATH 177, 2023
1
$20 with probability 0.2; lose $10 with probability 0.7; or enter into a bonus round with
probability 0.1. In the bonus round I can choose options 'c' of 'd'. If I choose option 'c'
then one of two things happen: I could get $200 with probability 0.05; or get $20 with
probability 0.95. If I choose option 'd' I would collect $30.
(b) I can choose either 'A' or 'B'. If I choose 'A', there is a 50% chance I get a choice between
'C' and 'D' (i.e. a decision node). If I choose 'C' I get $400 with probability 0.6 or $800
with probability 0.4. If I choose 'D' I then get $500. If I choose 'A' but did not get to
choose between 'C' and 'D' then I instead get a choice between 'E' and 'F'. If I choose 'E'
I get $300 with probability 0.7 or $1000 with probability 0.3. If I choose 'F' I then get
$600.
If I choose 'B' I get $400 with probability 0.8 or a choice between 'G' and 'H'. If I choose 'G'
I get an equal chance of getting $200 or $700. If I choose 'H' I get $1200 with probability
0.4 or $0 with probability 0.6.
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Given the descriptions about two decision trees.
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