**JD Long**posed a challenge:

Great Bayesian exercise! So let’s say criminals are .5% of society. And the accuracy is 90%. What’s the probability that a person is a criminal if this algo tags them? https://t.co/XtX3OSwUsf— JD Long (@CMastication) March 6, 2019

The tweet is related to a paper discussed in

**this article by Calling Bull**. Imagine that such an algorithm were applied to the real world. What is the probability that a person is a criminal if the algorithm says so?

JD provided two data points:

• We assume that criminals are 0.5% of the population

• The accuracy of the algorithm is 90%

In the

**thread**there are responses that answer the question using conditional probability formulas. Here's a little secret: I loathe formulas. Particularly when I can reason with an image instead; I may one day write a book about that, although

**is already out there, and you should get a copy. I prefer quick heuristics and visuals.**

*Math with Bad Drawings*For my quick back-of-the-napkin-and-not-that-precise exercise on conditional probability I needed two other figures:

• The population: let's assume that we're in the U.S, so it's 325 million (you may not need the population if you use formulas, but it's useful for the diagram.)

• The false positive rate: how often the algorithm tags a person as a criminal even if that person

*is not*a criminal. After reading

**this**I guessed a false positive rate of around 6%.

Here's the resulting

**tree diagram**; the probability of your being a criminal if the algorithm tags you as such is roughly only 7%:

*aren't*criminals but are still wrongly tagged by the algorithm) and 1,462,500 (people who

*are*criminals and are correctly identified by the algorithm). Adding up those two figures you get the total number of people tagged as criminals,

*regardless of whether they are indeed criminals or not*: 20,865,000.

Of those, 93% (the 19,402,500) aren't criminals. The chance of false positives is enormous: if a photo is tagged as depicting a criminal, 9 out of 10 times that person won't be a criminal at all.

I double-checked the calculation using round numbers, beginning with a sample of 10,000 people; quants in the room, please

**let me know**if I missed something:

**websites**and books that cover heuristics and diagrams for reasoning. To get started, I'd recommend Gerd Gigerenzer's

**or Judea Pearl's**

*Risk Savvy***. If you are a journalist or a graphic designer, I**

*The Book of Why**strongly*recommend books like these, as we often get probability wrong. You'll enjoy them.