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The Prosecutor’s Fallacy: How Bad Math Almost Ruined Lives

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In 1963, a petty neighborhood robbery in Los Angeles set a legal precedent on using probabilistic evidence in trials. This case, involving an elderly woman named Juanita Brooks, who was attacked and robbed by a blonde woman, and John Bass, a witness who saw a blonde woman with a ponytail and a Black man with a beard in a yellow car, would highlight a crucial issue: the misuse of probability in court, known as the prosecutor’s fallacy.

The police linked the robbery to an interracial couple, Janet and Malcolm Collins, who filled up their yellow car at a nearby gas station. Despite neither witness positively identifying them from photos, the shaky alibi and Malcolm’s criminal record led to their arrest. Desperate to secure a conviction, Prosecutor Ray Sinetar turned to probability.

Sinetar enlisted a professor to apply the product rule, which multiplies independent event probabilities to find their combined likelihood. He fabricated probabilities for details provided by witnesses:

  • A Black man having a beard: 1 in 10.
  • A man having a mustache: 1 in 4.
  • A White woman having blonde hair: 1 in 3.
  • A woman having a ponytail: 1 in 10.
  • An interracial couple in a car: 1 in 1,000.
  • The car being yellow: 1 in 10.

The professor calculated a 1 in 12 million chance that all six factors would occur together, implying Janet and Malcolm were the only possible culprits in Los Angeles. Sinetar convinced the jury this “new math” was stronger than “proof beyond a reasonable doubt,” leading to the Collinses’ conviction for second-degree robbery.

However, this was flawed math. The factors were not independent; the probabilities were made-up guesses. On appeal, the Collinses argued the misuse of probabilistic evidence. The appellate court agreed, noting that even if all assumptions were correct, the probability of the defendants’ innocence exceeded 40 percent, establishing reasonable doubt.

This case, a stark example of the prosecutor’s fallacy, set a precedent: probabilistic evidence must be based on reliable data and sound methodology. It highlighted the dangers of using arbitrary numbers to secure convictions and underscored the importance of critical thinking.

Dive deeper into how cognitive biases and flawed reasoning shape our decisions by reading Think Like a Black Sheep. This book will guide you in understanding these hidden pitfalls and help you navigate the manipulations we face daily. Start your journey to greater awareness and critical thinking today. Read more in Think Like a Black Sheep and see the world with new eyes

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