Prosecutor's Fallacy Examples

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One of the purposes of a legal system is to ensure that those who violate the laws are punished in a just and fair manner. As a result, criminal trials rely on the maxim, “actori incumbit onus proband”, which translates to: “The burden of proof rests on the party who advances a proposition affirmatively”.1 This means it is the job of the prosecutor to prove the defendant is guilty beyond reasonable doubt. However, sometimes the evidence provided is misinterpreted causing miscarriages of justice. One example is known as the Prosecutor's Fallacy.

I chose to explore the Prosecutor's Fallacy because I intend to study law and practice as a barrister. The Prosecutor's Fallacy is not just a theoretical fallacy dreamt up in hypothetical examples, but is a real and live issue that has caused the incarceration of
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With this knowledge in hand we can now explore the Prosecutor's Fallacy. To show how both the Prosecutor's Fallacy occurs and to prove why the fallacy is wrong, two hypothetical examples have been given below. The hypothetical examples are then followed by two real life cases to show how this fallacy has caused miscarriages of justice.

Example One – Winning the Lottery
A woman wins the lottery. The calculated odds of winning the lottery were one in a million. As a result, she is accused by an angry mob of rigging the lottery. They argue: “The probability she won (W), given that she did not cheat (NC), is one in a million. Therefore, since she won, she must have cheated due to the low probability of winning without cheating.” Although this argument appears to have merit, when broken down into mathematical notation its flaws are revealed. As we see below:

The probability she won, given that she did not cheat (what happened) is seen as this:
The probability that she did not cheat, given that she won (the mob's accusation) is seen as