What Are the Chances Luigi is Guilty? A Lesson in Bayesian Thinking

Video script:

Luigi Manjioni’s murder trial surrounding healthcare insurance CEO Brian Thompson has taken the world by storm, with endless speculation swirling around. But let’s take a step back and remind ourselves of a fundamental principle: “innocent until proven guilty.”

If Luigi’s DNA is found at the crime scene, what do you think the likelihood of him being guilty is? Let’s break it down using Bayes' Rule.

Assuming no prior evidence besides a positive DNA test, let’s assume the following:
1. There are roughly 350 million people in the USA, so the pool of potential suspects is vast.
2. A false positive rate of roughly 1 in 3 million meaning the probability of incorrectly matching an innocent person’s DNA to a crime scene is exceptionally low.
3. If he is guilty, then the DNA will match with 100% (for simplicity).

So, what does Bayes’ Rule tell us?

Even with a DNA match, the chance Luigi is guilty turns out to be only about 0.85%—or 1 in 118 people. Surprising, right? Narrow the pool to just New York’s 8 million residents, and the probability rises to about 25%—or 1 in 4 people.

Of course these numbers are merely just for illustrative purposes. As new evidence emerges, such as notebook entries, fake IDs, an alibi, and ballistics, these probabilities will shift. Bayesian thinking highlights how evidence updates beliefs but doesn’t replace the careful deliberation required in the legal system.

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