Here is a newspaper passage describing Mad Unicorn Disease: Recent reports suggest that Mad Unicorn Disease...

 

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Here is a newspaper passage describing Mad Unicorn Disease: "Recent reports suggest that Mad Unicorn Disease is on the rise. Every tenth person in the world now carries the disease, although 25% of the carriers report no symptoms. The characteristic symp- toms for the most recent viral mutation of the disease are very dis- tinct, so authorities can now safely assume that non-carriers never report any false symptoms. A hospital-administered test is reason- ably accurate, but not perfect: it detects the disease in every tenth non-carrier." (a) Does the newspaper passage contain enough information to find the conditional probability that a person has Mad Unicorn Disease, given that the person tests positive for the disease? If not, please identify what information is missing and invent any reasonable-looking quantities for any missing value(s) that you may need. (4 marks) (b) Based on your answer to (a) (if needed), calculate the condi- tional probability that a person has Mad Unicorn Disease, given that the person tests positive for the disease. (7 marks) (c) Based on your answer to (a) (if needed), calculate the condi- tional probability that a person has Mad Unicorn Disease, given that the person reports no symptoms. (7 marks) (d) Based on your answer to (a) (if needed), calculate the condi- tional probability that a person tests positive for Mad Unicorn Disease, given that the person reports no symptoms. (7 marks) Here is a newspaper passage describing Mad Unicorn Disease: "Recent reports suggest that Mad Unicorn Disease is on the rise. Every tenth person in the world now carries the disease, although 25% of the carriers report no symptoms. The characteristic symp- toms for the most recent viral mutation of the disease are very dis- tinct, so authorities can now safely assume that non-carriers never report any false symptoms. A hospital-administered test is reason- ably accurate, but not perfect: it detects the disease in every tenth non-carrier." (a) Does the newspaper passage contain enough information to find the conditional probability that a person has Mad Unicorn Disease, given that the person tests positive for the disease? If not, please identify what information is missing and invent any reasonable-looking quantities for any missing value(s) that you may need. (4 marks) (b) Based on your answer to (a) (if needed), calculate the condi- tional probability that a person has Mad Unicorn Disease, given that the person tests positive for the disease. (7 marks) (c) Based on your answer to (a) (if needed), calculate the condi- tional probability that a person has Mad Unicorn Disease, given that the person reports no symptoms. (7 marks) (d) Based on your answer to (a) (if needed), calculate the condi- tional probability that a person tests positive for Mad Unicorn Disease, given that the person reports no symptoms. (7 marks)