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Rather than a made up brain teaser, a real court case from 1964: http://www.law.berkeley.edu/faculty/sklansky/evidence/evidence/cases/Cases%20for%20TOA/People%20v.%20Collins.htm (Spoiler alert: The court record provides an answer to this 'brainteaser', but their answer may or may not be correct - they are judges trained in the legal profession, after all.)
If the characteristic individual probability of each item testified to is:
A. Partly yellow automobile 1/10
B. Man with mustache 1/4
C. Girl with ponytail 1/10
D. Girl with blond hair 1/3
E. Negro man with beard 1/10
F. Interracial couple in car 1/1000
Never mind the fact that the probabilities were entirely made up by the prosecution with the disclaimer that the jury was free to substitute whatever they felt the probability of each attribute was. If the probabilities listed were accurate, what's the probability that the defendants are innocent? Based on that probability, do you convict them?
On June 18, 1964, about 11:30 a.m. Mrs. Juanita Brooks, who had been shopping, was walking home along an alley in the San Pedro area of the City of Los Angeles. She was pulling behind her a wicker basket carryall containing groceries and had her purse on top of the packages. She was using a cane. As she stooped down to pick up an empty carton, she was suddenly pushed to the ground by a person whom she neither saw nor heard approach. She was stunned by the fall and felt some pain. She managed to look up and saw a young woman running from the scene. Immediately after the incident, Mrs. Brooks discovered that her purse, containing between $35 and $40 was missing.
About the same time as the robbery, John Bass, who lived on the street at the end of the alley, was in front of his house watering his lawn. His attention was attracted by "a lot of crying and screaming" coming from the alley. As he looked in that direction, he saw a woman run out of the alley and enter a yellow automobile parked across the street from him. He was unable to give the make of the car. The car started off immediately and pulled wide around another parked vehicle so that in the narrow street it passed within 6 feet of Bass. The latter then saw that it was being driven by a male Negro, wearing a mustache and beard. In his testimony Bass described the woman who ran from the alley as a Caucasian, slightly over 5 feet tall, of ordinary build, with her hair in a dark blonde ponytail, and wearing dark clothing. He further testified that her ponytail was "just like" one which Janet had in a police photograph taken on June 22, 1964.
On the day of the robbery, Janet was employed as a housemaid in San Pedro. Her employer testified that she had arrived for work at 8:50 a.m. and that defendant had picked her up in a light yellow car about 11:30 a.m. On that day, according to the witness, Janet was wearing her hair in a blonde ponytail but lighter in color than it appeared at trial.
If the characteristic individual probability of each item testified to is:
A. Partly yellow automobile 1/10
B. Man with mustache 1/4
C. Girl with ponytail 1/10
D. Girl with blond hair 1/3
E. Negro man with beard 1/10
F. Interracial couple in car 1/1000
Never mind the fact that the probabilities were entirely made up by the prosecution with the disclaimer that the jury was free to substitute whatever they felt the probability of each attribute was. If the probabilities listed were accurate, what's the probability that the defendants are innocent? Based on that probability, do you convict them?
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