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to help students understand and pass exams such as Functional Skills Maths, GCSE Maths and A Level Maths
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to help students practice with online maths quizzes
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to show how maths is significant in many key businesses and services
How courts in UK can mislead juries using incorrect Maths
To understand what happens let's simplify the numbers and assume the following scenario (represented in diagram shown below)
a crime has been committed by 1 adult in a village that has a population of 100 adults
criminal has left a DNA sample at the scene of the crime
via an expert source DNA match for this sample is 1 in 10
1 adult from the village (with a DNA match) is in court on trial for this crime
So a crime is committed and the criminal has left a sample of DNA at the scene.
The match probability of this sample is the probability that , if you pick someone at random, their DNA would match the crime sample.
So it is the probability of a match, if innocent.
(in our example this is 9/99, less than 10%)
It is NOT the probability of innocence , if a match
(in our example this is 9/10, equal to 90%)
To assume this would be to commit the Prosecutors fallacy!
In this case that would be incorrectly advising the jury that the probability of INNOCENCE is less than 10%.
The two probability calculations are related via bayes formula, but they are not the same!
(hence, though a jury is often persuaded otherwise, DNA evidence alone is not sufficient to determine INNOCENCE at court trials)
See link below for more examples from Professor Ray Hill including incredible courts cases where Professor Ray Hill helped courts understand Maths correctly which subsequently assisted with the release of mothers who were incorrectly convicted of murder in the UK as recently as the 1990's after tragically experiencing 2 cot deaths or more?
Mathematics in the Courtroom, Ray Hill | LMS Popular Lectures 2013
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