The Prosecutor's Fallacy is a type of invalid interpretation of a valid statistic.Consider a person who is accused of cheating on a lottery. A prosecutor may point out that there was only a 1 in 10,000,000 chance of the person winning, so they must have cheated. This may neglect the fact that 20,000,000 tickets were sold and someone had to win.
As another example, consider a crime that is investigated by looking at a DNA database with 1,000,000 samples. A match is found and at trial the prosecutor may state there was only a 1 in 10,000 chance of the match. They fail to mention that such margin of error is extremely significant considering the large number of samples tested. The Prosecutor's Fallacy is also used by the defence in many cases and is not specific to law. It has implications for scientific analysis, business decisions and professional advice.

Type  Statistical Fallacy  Definition  An invalid interpretation of a valid statistic.  Common Cause  Using a specific probability while ignoring a more general probability.
Neglecting the importance of margin of error and sample size.Pointing out that the sequence of events that make someone innocent have a low probability without considering that the sequence of events that make someone guilty are equally improbable.  Related Concepts  
Thinking
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