**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.

## False Positives

As another example, consider a crime that is investigated by scanning a database of 10,000,000 people. A match is found to a suspect and at trial the prosecutor may state there was*only*a 2% false positive rate. They fail to mention that this is extremely significant whereby a total of 200,000 false positives would be generated by scanning all 10,000,000 entries.

Number of False Positives = Population Size × False Positive Rate

Number of False Positives = 10,000,000 × 0.02

Number of False Positives = 200,000 false positives

Number of False Positives = 10,000,000 × 0.02

Number of False Positives = 200,000 false positives

## Significance

The Prosecutor's Fallacy is not specific to law. It has implications for scientific analysis, business analysis, problem solving and decision making.Overview: Prosecutors Fallacy | ||

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 | Base Rate FallacyStatistical FallaciesCognitive Biases |