People v. Collins

The People of the State of California v. Collins was a 1968 jury trial in California, USA that made notorious forensic use of mathematics and probability.

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 (A) 1 in 10
Man with moustache (B) 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
By multiplying the probability of all events, the chance of a couple fitting all these distinctive characterisistics are 1 in 12 milllions.
The jury returned a verdict of guilty.

Appeal:
Black man with beard (A) 1 in 10
Man with moustache (B) 1 in 4

The argument on events A and B was "most men with a beard also have a mustache". So if you observe a Black man with beard, the chances are no long 1 in 4 that the man you observe has a mustache.

The population of the crime area was several millions, which means that there could be 2 or 3 couples with the description.