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Q&A

What story and one-digit Natural Numbers explain Bayes' Theorem chart most simply?

+2
−1

Some students have sniveled that most examples of Bayes' Theorem use non-integer numbers. I want to try a Bayes' Theorem chart that uses just single digit Natural Numbers $\le 9$. To complete the table below most comfortably for teenagers,

  1. what are the simplest stories?

  2. what natural numbers ≤ 9 contrast the base rate fallacy the most? Please don't repeat a number.

The biggest number in this similar question still uses two digits, and rehashes the common example of letting D be be a disease and $H_0$ be a negative (diagnostic) test result. What other $H_0, D$ are more intuitive? Green denotes true positive and negative, red false positive and negative.

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

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3 comments

I posted at https://math.codidact.com/posts/280742 about the miffed Mathjax. DNB‭ 27 days ago

How are you quantifying "contrast the base rate fallacy"? Peter Taylor‭ 27 days ago

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