People v. Collins was a 1968 trial in the Supreme Court of California that reversed the convictions of Janet and Malcolm Collins by a jury in Los Angeles of second-degree robbery. The events that led to the original conviction were as follows:
On June 18, 1964, Mrs. Juanita Brooks was walking home along an alley in San Pedro, City of Los Angeles. She was suddenly pushed to the ground, and she saw a young woman running, wearing “something dark.” She had hair “between a dark blond and a light blond,”. After the incident, Mrs Brooks discovered that her purse, containing between $35 and $40, was missing.
At about the same time, John Bass, who lived on the street at the end of the alley, saw a woman run out of the alley and enter a yellow automobile driven by a black male wearing a moustache and beard.
The prosecutor (of the jury trial) brought a statistician to prove the crime using the laws of probability. The expert hypothesised the following chances and made his calculations.
| Characteristic | Probability | |
| 1 | Yellow automobile | 1/10 |
| 2 | Man with moustache | 1/4 |
| 3 | Girl with poleytail | 1/10 |
| 4 | Girl with blondehair | Girl with blonde hair |
| 5 | Interracial couple in a car | 1/10 |
| 6 | Interracial couple in car | 1/1000 |
The profession used the product rule (the AND rule) of probability to prove the case. Multiplying all the probabilities, he concluded that the chance for any couple to possess the characteristics of the defendants is 1/12,000,000! Note that such multiplication is only possible if the individual probabilities are independent.
But the statistician (and the jury) convenient ignored a few things:
1) The validity of the probabilities. Those were his ‘inventions’ without any support from data.
2) The events (characteristics) were not independent from each other. More likely than not, the person with a beard has a moustache.
3) Once, a blond girl and a black man with a beard were counted, talking about the low probability of an interracial couple in a car is wrong. Think about it—the probability of an interracial couple, given one is a blond girl and another is a bearded black man, must be close to 1.
References
People v. Collins: Justia US Law
The Worst Math Ever Used In Court: Vsauce2
A Conversation About Collins: William B. Fairley; Frederick Mosteller
