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Q&A

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

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Closed as duplicate by Monica Cellio‭ on Jun 6, 2021 at 23:55

This question has been addressed elsewhere. See: What story and one-digit Natural Numbers explain Bayes' Theorem chart most simply?

This question was closed; new answers can no longer be added. Users with the reopen privilege may vote to reopen this question if it has been improved or closed incorrectly.

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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2 comments

Does the code support an array here? tommi‭ 21 days ago

This appears to be exactly the same as your earlier question https://math.codidact.com/posts/280741 , and certainly suffers the same flaw that I raised then in the comments which makes it unanswerable. Peter Taylor‭ 19 days ago

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