1a) Suppose that Nate tested positive for hepatitis B. Thetest catches 99% of he

Question

1a) Suppose that Nate tested positive for hepatitis B. Thetest catches 99% of hepatitis cases, so why is Nate not 99% certainthat he has hepatitis?

1b) Jane thinks that the sentance "A woman will be electedpresident in 2024." has a better than even chance of beingtrue. Quantify her degree of belief.

1c) Explain why logic is prescriptive and not descriptive. Why is this a logical error: "If it walks like a duck and quackslike a duck, then it is a duck?"

1d)Precipitation is any form of water from the sky (snow, rain,hail, sleet, etc.). Why is this a probability erroe."It's winter, so the probability of snow tomorrow is greaterthan the probability of precipitation tomorrow."

1e) Ed thinks there is a 90% chance that angels exist and Ellenthinks there is only 1% chance. Why is this not a probabilityerror?

Explanation / Answer

a. Nate cannot be 99% sure that he has Hepititus, because outof the 1% that test positive, less than 100% actually haveHepititus. There is room for the possibility that the test iswrong. b. Jane believes that this chance is greater than 50%. c. Logic is not descriptive because it is not subjective tothe object. The error in the logic is that it assumesthat the ONLY things to walk and quack like ducks areducks. d. The probability of snow can never be more than theprobability of precipitation because snow is a subset ofprecipitation. If there were a 0% chance of rain, hail andsleet, then at most, the probability of snow would be equal to theprobability of precipitation, but never more. e. This is not a probability error because this is what peoplebelieve. They are not basing their beliefs on observabledata.

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