The People of the State of California v. Collins[1] was a 1968 jury trial in California, USA that made notorious forensic use of mathematics and probability.
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Bystanders to a robbery in Los Angeles testified that the perpetrators had been a black male, with a beard and moustache, and a caucasian female with blonde hair tied in a ponytail. They had escaped in a yellow motor car.
After testimony from an "instructor in mathematics" about the multiplication rule for probability, the prosecutor invited the jury to consider the probability that the accused pair, who fitted the description of the witnesses, were not the robbers. Even though the "instructor" had not discussed conditional probability, the prosecutor suggested that the jury would be safe in estimating:
| Black man with beard | 1 in 10 |
| Man with moustache | 1 in 4 |
| White woman with pony tail | 1 in 10 |
| White woman with blonde hair | 1 in 3 |
| Yellow motor car | 1 in 10 |
| Interracial couple in car | 1 in 1000 |
The jury returned a verdict of guilty.
The Supreme Court of California set aside the conviction, criticising the statistical reasoning and disallowing the way the decision was put to the jury. In their judgment, the justices observed that mathematics:
The statistical reasoning at first instance was criticised as it failed to take into account the probable dependencies between the characteristics, for example, bearded men commonly sport moustaches.
It has also been criticised as an example of the prosecutor's fallacy.[2][3]
The original decision has been supported by a minority of writers.[4]