What is the prosecutor's fallacy, and how did it affect the Sally Clark case?
A tiny chance of a coincidental match is not the chance that the matching person is innocent: mixing them up has helped convict people wrongly.
It is the mistake of treating two different chances as if they were one. The chance that an innocent person would match the evidence by coincidence is not the same as the chance that the person who matches is innocent. When applied to the results of statistical tests such as DNA tests in court, the is called the prosecutor's fallacy. It assumes that the probability of a random match equals the probability that the is innocent.
A simple example shows the gap. Suppose the perpetrator has a blood type shared by 10% of the population, and a suspect is arrested who has that blood type. A prosecutor might claim on that basis alone that the is 90% likely to be guilty. But if 1,000 people live in the town, 100 have that blood type and only one is the culprit. Based only on the blood type, the chance that the defendant is guilty is 1%, far less than 90%.
Step 1: 1,000 people live in town
One of them committed the crime.
Step 2: 10% share the blood type
That is 100 people, including the culprit.
Step 3: The suspect is one of the 100
On blood type alone, 1 in 100 is guilty.
Step 4: 1%, not 90%
Other evidence has to do the rest.
The mistake has had real victims. Sally Clark, an English solicitor, was found guilty in November 1999 of the murder of her two infant sons, in what became a . The prosecution relied on flawed statistics from the paediatrician Roy Meadow, who testified that the chance of two children from an affluent family suffering , sudden infant death syndrome, was 1 in 73 million. Many press reports said that this was the probability that Clark was innocent. Even if the figure had been valid, it should not have been read that way.
Her convictions were overturned in January 2003. The had said that there was no statistical basis for the figure and expressed concern at the misuse of statistics in the courts.
Try it
How many people match by chance?
y = 0.1x + 0
Challenge · Set the chance to 0.1 (10%). In a town of 1,000, how many people match, and so how likely is it that any one of them is the culprit?
Quiz me
0/3
Recap
“How rare is the match?” and “how likely is it that the matching person is guilty?” are different questions.
💡 A trick to remember it · A rare fingerprint in a big crowd still has company: count the people who match before you count the odds.
Surprising fact · Sally Clark's convictions were overturned in January 2003, and a review of hundreds of other cases followed.
Connects to
- 🌳 How did a genealogy website help catch the Golden State Killer?
- 🎲 What does “a one in a billion DNA match” actually mean?
- ⚖️ Why is a suspect treated as innocent until proven guilty?
- 🚨 How can a 95%-accurate test be wrong 98% of the times it says yes?
- 🧮 Why does a positive result from a 99% accurate test often mean so little?
- Conditional probability
Sources (2)
No source, no claim. Every fact in this lesson (16 claims) cites at least one of these.