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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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Two professional athletes and six fans are eating at a restaurant table. Both of the professional athletes are wearing their jerseys, while only half of the fans are wearing jerseys. Given a person at the table wearing a jersey, what is the probability that they are a professional athlete?

I don't know why you think that students understand BT better with single-digit numbers. Seems to me that with a hundred fans it becomes far clearer how unlikely it is that a jersey-wearing person is an athlete even though all of the athletes are wearing jerseys. But you do you.

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  • $\begingroup$ Hi. Thanks. Students still can't intuit Bayes's Theorem! " If you keep doing the same thing, you'll get the same results." I just want to try something else $\endgroup$
    – user15364
    Jan 29, 2021 at 4:03

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