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.

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


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.

  • $\begingroup$ 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 $\endgroup$
    – TOI.V
    Jan 29 at 4:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.