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

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.

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

## 1 Answer

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.

• 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 – codidact Jan 29 at 4:03