The Language of Argument
2 4 3 The Language of Probability heuristics when the situation is nonstandard—that is, when the situation is complex or out of ...
2 4 4 C HaP Te r 1 1 ■ C h a n c e s We can make our probability claims more precise by using numbers. Sometimes we use percenta ...
2 4 5 a P r i o r i P r o b a b i l i t y Notice that in coming to our conclusion that there is one chance in thirteen of random ...
2 4 6 C HaP Te r 1 1 ■ C h a n c e s Some Rules of Probability Suppose you have determined the probability that certain simple e ...
2 4 7 S o m e ru l e s o f P r o b a b i l i t y This makes sense because there are forty-eight out of fifty-two ways of not dra ...
2 4 8 C HaP Te r 1 1 ■ C h a n c e s Rule 2G: Conjunction in General. Given two events, the probability of their both occurring ...
2 4 9 S o m e ru l e s o f P r o b a b i l i t y half the class is female and exactly half the class is over nineteen and the ag ...
2 5 0 C HaP Te r 1 1 ■ C h a n c e s heads at least once, and thus after eight tosses there should be a 400 per- cent chance. In ...
2 5 1 S o m e ru l e s o f P r o b a b i l i t y We need to calculate probabilities of combinations in a different way. For exam ...
2 5 2 C HaP Te r 1 1 ■ C h a n c e s Suppose there are two little lotteries in town, each of which sells exactly one hundred tic ...
2 5 3 Bayes’s Theorem bayeS’S THeorem Although dice and cards provide nice, simple models for learning how to calculate probabil ...
2 5 4 C HaP Te r 1 1 ■ C h a n c e s includes the true positives plus the false positives, which are those who test positive but ...
2 5 5 B a y e s ’ s T h e o r e m Finally, we apply Rule 2G to item 4 and get: BT: Pr 1 h 0 e 25 Pr 1 h 23 Pr 1 e 0 h 2 (^3) Pr ...
2 5 6 C HaP Te r 1 1 ■ C h a n c e s Colon Cancer Not Colon Cancer Total Test Positive Do Not Test Positive Total 100,000 This p ...
2 5 7 ba y e s ’ s T h e o r e m Similarly, we can fill out the third column by dividing the total number of people without colo ...
2 5 8 C HaP Te r 1 1 ■ C h a n c e s Tables like these work by dividing the population into groups. We already learned some name ...
2 5 9 ba y e s ’ s T h e o r e m those symptoms is 0.3, then a positive test result does show that the pa- tient probably has ca ...
2 6 0 C HaP Te r 1 1 ■ C h a n c e s What would Wendy’s chances of having colon cancer be if the other probabilities remained t ...
2 6 1 B a y e s ’ s T h e o r e m NOTES (^1) Amos Tversky and Daniel Kahneman, “Extensional Versus Intuitive Reasoning: The Conj ...
97364_ch11_ptg01_239-262.indd 262 15/11/13 10:58 AM some third party content may be suppressed from the eBook and/or eChapter(s) ...
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