As Jonathan Holbrook wrote in a blog post about the prosecutor’s fallacy:
The key to understanding the fallacy is to recognize that we are talking about two fundamentally different questions: Assuming the person is innocent, what is the likelihood that his DNA would be a match to the sample from the crime scene? Assuming that the DNA is a match, what is the likelihood that the person is innocent?
The prosecutor’s fallacy takes the answer to the first question and uses it is an answer to the second question. That’s flawed logic, because you’re actually talking about two very different concepts: random match probability vs. source probability.
So, does a prosecutor commit the prosecutor’s fallacy and violate the defendant’s rights by arguing that the defendant had a better chance of winning Powerball than the DNA on the victim not coming from him? That was the question addressed by the Colorado Court of Appeals in its recent opinion in People v. Ortiz, 2026 WL 3253603 (Colo. App. 2026).
In Ortiz, Josias Deonicio Ortiz was charged with seven offenses relating to sexual assault on a child (“B.B.”). At trial,
An expert with the Colorado Bureau of Investigation tested DNA samples taken from B.B.’s neck, face, and clothing. The expert testified that she ran two types of tests on the DNA samples: (1) the “total human” DNA test, which focuses on results specific to individual potential contributors; and (2) the YSTR DNA test, which excludes female DNA and provides male-specific results.
Thereafter,
The expert discussed the statistical conclusions that she drew using a “likelihood ratio,” explaining that the mixture was “approximately 1.8 septillion … times more likely to be observed if it originated from [B.B.], Mr. Ortiz, and an unknown, unrelated individual, than if it had originated from [B.B.], and two unknown, unrelated individuals,” which strongly supported “the proposition that Mr. Ortiz is included as a potential contributor to that mixture profile.”
During closing arguments, the prosecutor told the jurors:
I understand this is confusing, but it is 1.8 septillion times more likely that…14 percent is the defendant, 85 percent is [B.B.], and one percent some random person, than it for it to be two random males.
There was a Powerball recently. You had one in 2.92 million chances of winning it, okay? You had a better chance of winning that Powerball a hundred time[s] over than it not being him on [B.B.]. That is what that number looks like. That is what 1.8 septillion looks like. It is a huge number.
In finding that this was not reversible error, the court ruled that
The prosecutor’s closing arguments drew on the DNA expert’s testimony and the likelihood ratio. Although the prosecutor used a rhetorical device to comment on the evidence, we perceive no misconduct. It was proper for her to reference the likelihood that Ortiz contributed to the mixture of the DNA sample taken from B.B. And the prosecutor’s comments didn’t intentionally misstate the evidence or the inferences the jury could draw from it.
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