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9. Scientists have discovered that drinking large amounts of Red Bull is correlated with a disease called redbullitis, whose symptoms involve acting like an enraged bull. Scientists don't think that drinking Red Bull causes redbullitis. Rather, the leading hypothesis is that some people have a gene that both predisposes them to crave Red Bull, and causes them to get redbullitis. Nonetheless, there is a correlation: 60% of people who drink red bull get redbullitis, while 60% of people who don't drink red bull don't get redbullitis. Isabella wants to drink Red Bull (+5 utility), but she also doesn't want to get redbullitis (-10 utility). She constructs the following decision table, where u1-U4 are the utilities of each outcome: Get redbullitis Don't get redbullitis Drink U1 U2 Red Bull Don't drink Red Bull U3 U4 a. Find the values of u1-u4 based on the above information. b. Find the expected utilities of each choice using the given evidential probabilities. What does (evidential) decision theory tell her to do? c. What would the causal decision theorist say about this case?

9. Scientists have discovered that drinking large amounts of Red Bull is correlated with a disease called redbullitis, whose symptoms involve acting like an enraged bull. Scientists don't think that drinking Red Bull causes redbullitis. Rather, the leading hypothesis is that some people have a gene that both predisposes them to crave Red Bull, and causes them to get redbullitis. Nonetheless, there is a correlation: 60% of people who drink red bull get redbullitis, while 60% of people who don't drink red bull don't get redbullitis. Isabella wants to drink Red Bull (+5 utility), but she also doesn't want to get redbullitis (-10 utility). She constructs the following decision table, where u1-U4 are the utilities of each outcome: Get redbullitis Don't get redbullitis Drink U1 U2 Red Bull Don't drink Red Bull U3 U4 a. Find the values of u1-u4 based on the above information. b. Find the expected utilities of each choice using the given evidential probabilities. What does (evidential) decision theory tell her to do? c. What would the causal decision theorist say about this case?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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页码:3/4 9. Scientists have discovered that drinking large amounts of Red Bull is correlated with a disease called redbullitis, whose symptoms involve acting like an enraged bull. Scientists don't think that drinking Red Bull causes redbullitis. Rather, the leading hypothesis is that some people have a gene that both predisposes them to crave Red Bull, and causes them to get redbullitis. Nonetheless, there is a correlation: 60% of people who drink red bull get redbullitis, while 60% of people who don't drink red bull don't get redbullitis. Isabella wants to drink Red Bull (+5 utility), but she also doesn't want to get redbullitis (-10 utility). She constructs the following decision table, where u1-u4 are the utilities of each outcome: Get redbullitis Don't get redbullitis Drink u1 u2 Red Bull Don't drink u3 U4 Red Bull a. Find the values of u1-u4 based on the above information. b. Find the expected utilities of each choice using the given evidential probabilities. What does (evidential) decision theory tell her to do? c. What would the causal decision theorist say about this case?
Transcribed Image Text:页码:3/4 9. Scientists have discovered that drinking large amounts of Red Bull is correlated with a disease called redbullitis, whose symptoms involve acting like an enraged bull. Scientists don't think that drinking Red Bull causes redbullitis. Rather, the leading hypothesis is that some people have a gene that both predisposes them to crave Red Bull, and causes them to get redbullitis. Nonetheless, there is a correlation: 60% of people who drink red bull get redbullitis, while 60% of people who don't drink red bull don't get redbullitis. Isabella wants to drink Red Bull (+5 utility), but she also doesn't want to get redbullitis (-10 utility). She constructs the following decision table, where u1-u4 are the utilities of each outcome: Get redbullitis Don't get redbullitis Drink u1 u2 Red Bull Don't drink u3 U4 Red Bull a. Find the values of u1-u4 based on the above information. b. Find the expected utilities of each choice using the given evidential probabilities. What does (evidential) decision theory tell her to do? c. What would the causal decision theorist say about this case?
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