$Probability/statistics$

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$Probability/statistics$

In a city with one hundred taxis, 1 is blue and 99 are green. A witness observes a hit-and-run by a taxi at night and recalls that the taxi was blue, so the police arrest the blue taxi driver who was on duty that night. The driver proclaims his innocence and hires you to defend him in court. You hire a scientist to test the witness’ ability to distinguish blue and green taxis under conditions similar to the night of accident. The data suggests that the witness sees blue cars as blue 99% of the time and green cars as blue 2% of the time. Write a speech for the jury to give them reasonable doubt about your client’s guilt. Your speech should not be longer than a page. Keep in mind that most jurors have not taken a probability course, so maybe you can use an illustration instead of just formula.

Probability

Kratos

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As you, the members of jury, know we hired a scientist to test the witness’ ability to distinguish blue and green taxis under conditions similar to the night of accident. The data suggests that the witness sees blue cars as blue 99% of the time and green cars as blue 2% of the time.
Assuming it is equally likely for any of our 100 taxies to have been involved in that accident, based on the scientific data, the witness would have seen a 2% of the 99 Green taxis as blue. That is 1.98 or roughly 2 taxis. The witness would seen the blue taxi as blue 99% of the time so that would be 0.99 or roughly 1 taxi. In other words, if those 100 taxis were all seen by the witness that night, the witness would have seen 3 as blue: one the real blue taxi and two green ones mistaken for blue. Puting it another way, scientifically it is twice as likely that the witness saw a green taxi as a blue one than the blue taxi as blue.
I would like to remind the jury that in a criminal court you shall convict when you are certain beyond a reasonable doubt. I think, a scientific I mind you, chance of 1 out 3 is no where near certainty beyond a reasonable doubt.

Shadmehr

29

$Probability/statistics$

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