Cognitive Biases

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# What is the Prosecutor's Fallacy?

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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.

## 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

## 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
Next: Base Rate Fallacy
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## Fallacies

A list of logical fallacies.

## Fallacy Fallacy

The fallacy of being too worried about fallacy.

## Cognitive Biases

A list of common cognitive biases explained.

## Broken Window Fallacy

An overview of the broken window fallacy.

## Overwhelming Exception

A common logical fallacy.

The definition of whataboutism with examples.

## Double Bind

The definition of a double bind with examples.

## False Equivalence

The definition of false equivalence with examples.

## Logic

A few logic terms explained.

## Law Of Excluded Middle

A classical law of logic first established by Aristotle.

## Fuzzy Logic

Logic that allows for partial truths.

## Logic vs Intelligence

The difference between logic and intelligence.

## Causality

The definition of causality with examples.

## Magical Thinking

The definition of magical thinking with examples.

## Scientism

The definition of scientism with examples.

## Mutually Exclusive

The definition of mutually exclusive with examples.

## False Balance

The definition of false balance with examples.
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## New Articles

Recent posts or updates on Simplicable.
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