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Q&A

What story and two-digit Natural Numbers best fit Bayes' Theorem chart?

+0
−2

To complete the table below most comfortably for teenagers,

  1. what are the simplest stories?

  2. what natural numbers $\le 99$ contrast the base rate fallacy the most? Please don't repeat a number.

I'm trying to improve on this question that uses two-digits just $\le 20$, because

  1. the Bayes table can be further contrasted using small with bigger ($\ge 20$) natural numbers. I don't know why Joseph O'Rourke stopped at 20, when he's using two digits anyways.

  2. Two-digit natural numbers don't fit the common story of letting D be a disease and $H_0$ be a negative (diagnostic) test result. You need natural numbers in the thousands to contrast the huge number of false positives with the teeny number of true positives. What $H_0, D$ are more intuitive? Green denotes true positive and negative, red false positive and negative.

$\begin{array}{r|cc|c} \text{Number of occurrences}&D &\lnot D &\text{Total}\\ \hline H_a &\color{green}{\Pr(D)\Pr(+|D)}&\color{red}{\Pr(D^C)\Pr(+|D^C)}&\text{add the 2 left entries}\ H_0 &\color{red}{\Pr(D)\Pr(-|D)}&\color{green}{\Pr(D^C)\Pr(-|D^C)}&\text{add the 2 left entries}\\ \hline \text{Total}&\text{add the 2 above entries}&\text{add the 2 above entries}&\text{two digit natural number} \end{array}$

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