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Probabilities and Courtroom Drama

April26

In 1964 a Los Angeles blond woman with a ponytail snatched a purse from another woman. The thief was spotted entering a yellow car driven by a black man with a beard and a mustache. The police eventually found a blond woman with a ponytail who regularly associated with a bearded and mustachioed black man who owned a yellow car, but there was no hard evidence linking them to the crime. In court, the prosecutor argued that the probability was so low that such a couple existed that the police must have found the actual culprits. The prosecutor assigned the following probabilities to the characteristics in question:

yellow car: 1 in 10 or 1/10
man with a mustache: 1/4
woman with ponytail: 1/10
woman with blond hair: 1/3
black man with beard: 1/10
interracial couple in a car: 1/1000

The prosecutor argued that the characteristics were independent, so the probability that a randomly selected couple would have them all would be:

(1 x 10) x (1 x 4) x (1 x 10) x (1 x 3) x (1 x 10) x (1 x 1000) = 1 in 12,000,000

This, he argued, was a probability so low that the couple must be guilty. The jury agreed and convicted them.” (extract from: Innumeracy-Mathematical Illiteracy and its Consequences)
BUT, the case was appealed to the California Supreme Court. What do you think the outcome was? (more in another post soon)

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The graph on the left (Coronavirus) is for a time period of 30 days, while the one on the right (SARS) is for 8 months! Very poor graphical comparison and hardly relevant, unless it is attempting to downplay the seriousness of the coronavirus?

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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