The Prosecutor's Fallacy happens when someone misinterprets the low odds of a specific innocent circumstance as sufficient to show that the accused's innocence

The Prosecutor's Fallacy happens when someone misinterprets the low odds of a specific innocent circumstance as sufficient to show that the accused's innocence is equally unlikely, because they have implicitly assumed that the odds of guilt are higher. Basic example: take a deck of cards and throw them in the air so the cards land in a random arrangement. If someone looks at the arrangement and says, "the odds against these cards landing in this specific arrangement are trillions to one, therefore someone must have arranged them like this deliberately," that's the Prosecutor's Fallacy. For a tragic example from real life, see the case of Sally Clark[1] who was wrongly convicted for the murder of her two baby sons. At trial, the only other possible explanation given for their deaths was Sudden Infant Death Syndrome (SIDS). A paediatrician testified that the odds of a single baby dying of SIDS were 1 in 8,500, so the probability of two specific babies dying in this way was the square of those odds (1 in 72 million). He concluded that the high improbability of this specific innocent circumstance meant that murder was a more likely explanation. There were several other problems with this testimony (not to mention the evidence presented), but this demonstrates the Prosecutor's Fallacy: the paediatrician misinterpreted the odds of two specific babies dying from SIDS as the odds of ever seeing SIDS claim a pair of babies. The odds he quoted are in the millions, but the number of two-child families is in the millions too; this means that such events will probably happen eventually, thanks to the Law of Truly Large Numbers[2]. [1] https://en.wikipedia.org/wiki/Sally_Clark https://en.wikipedia.org/wiki/Sally_Clark [2] https://en.wikipedia.org/wiki/Law_of_truly_large_numbers https://en.wikipedia.org/wiki/Law_of_truly_large_numbers