prompter: Explain the "prosecutor's fallacy" like I am five.

assistant: Imagine you have a bag of 100 marbles. You know that 90 of the marbles are blue and 10 are red.

You pick a marble out of the bag without looking, and it's blue.

The "prosecutor's fallacy" is when someone argues that the probability you picked a blue marble is 90% or very high. But that's wrong.

Once you've picked a marble, either it was blue (which it was) or red. The probabilities reset to either 100% or 0%.

The correct way to think about it is that before picking, there was a 90% chance of picking blue. But after picking, there is a 100% chance that you picked the marble you picked.

The "prosecutor's fallacy" gets its name because prosecutors sometimes commit this fallacy, arguing that the probability of someone's guilt is very high based on evidence, without taking into account that either they are guilty or not guilty, 100% or 0%, once the crime has occurred.

prompter: Why would a prosecutor want to perform a fallacy if they are interested in justice?

assistant: Fallacies aren't necessarily malicious. They are usually mental shortcuts that can lead to a wrong conclusion. The reason they are so common and dangerous is that they are often, but not always right and certainly not inherently right.
A prosecutor might unintentionally use it as a mental expedient to avoid using mental power on the problem. They are often overworked. If it's being done maliciously the least bad reason would be that in the US at least almost all court cases lead to a conviction of some sort. Sometimes this involves gamesmanship on the part of the prosecutor and plea deals, but often the court system mainly takes up cases with overwhelming evidence (such as caught-in-the-act drug possession cases) and the prosecutor gets into the mindset that the accused is always guilty. Finally, the possibility exists that the prosecutor simply isn't interested in justice.

assistant: The prosecutor's fallacy is a mistake that some people make when they're trying to figure out if someone did something wrong. Imagine you have a mystery box with candy inside. You know that a special kind of candy is only in the box if the person who put it there is guilty of a crime.

Now, imagine you opened the box and found the special candy. Some people might think that this means the person who put the candy in the box is definitely guilty of the crime. But that's not always true! There might be other boxes with the same candy, and the person who put it in the box you opened might not be the person who did the crime.

So, when people use the prosecutor's fallacy, they make a mistake by thinking that just because they found something, it means the person they think did the crime is definitely guilty. It's like jumping to a conclusion without looking at all the facts.

prompter: can you simplify that a bit? I'm only five.

assistant: The teacher caught Billy with something that was stolen from Bobby. No one knows for sure who stole but they do know Billy is holding it. The teacher assumes that Billy stole something because he is holding onto it. But this does not mean Billy stole it, he could have found it on the ground and just held onto it.

assistant: Sure! Imagine that you are playing a game of hide-and-seek with your friends. One of your friends, let's call them Susie, is found hiding in the same place that a toy was hidden. The toy is a special one that only a few people have, and Susie has it. The other kids might say that Susie took the toy, but that's not always true. It could be that someone else put the toy there and Susie just found it. Or maybe the toy was there before the game even started and Susie just happened to be hiding there.

This is like what the "prosecutor's fallacy" is talking about. Just because the evidence (the toy) is found with Susie, doesn't mean that Susie did something wrong. There could be other explanations for why the toy is there. So, we need to look at all the possible reasons before we make a decision. This is what the legal system is trying to do when they use this idea of the "prosecutor's fallacy".

assistant: Think of a game where you hide a toy in one of two boxes labeled "guilty" and "not guilty". Your friend has to guess which box the toy is in. The prosecutor's fallacy is like when your friend wrongly says that because the toy is in the "guilty" box, you must have done something wrong. Just like in a criminal trial, just because a person is found guilty doesn't mean they actually committed the crime. The prosecutor's fallacy is making the mistake of thinking that just because something happened, someone must be responsible for it. It's important to remember that a guilty verdict doesn't always mean the person did the crime.

prompter: This is still a bit complicated, I'm five remember?

assistant: A court, in law, is a part of the government in which people come together to decide how to apply the country's laws to a specific situation, especially when there is an argument over how to apply the law. Some disagreements a court may decide are whether a person is guilty of a crime, who is the legal owner of property, or who the children of two divorced parents should live with. A court is usually in a special building called a courthouse.
A trial is where two people or two groups of people argue in a court. 
A prosecutor is a lawyer who argues in a court that the defendant should be found guilty of a crime. Prosecutors usually represent the government.
A lawyer may help the defendant in trial. acting as a criminal defense attorney. 
Evidence is something that is used to support an argument. It gives examples of why something is true. 

When there is a trial the prosecutor can think the person they are trying to get found guilty of a crime is guilty for the simple fact that  they were there when something bad happened or that they are to blame even if there only a bit of evidence.