The Maths of a Jury and a Courtroom

Discussion in 'Mathematics' started by tango78, Jan 2, 2011.

1. tango78New commenter

Hi all,
I am teaching Maths in the context of Citizenship this half term and am really interested in the probabilities and associated Maths of the Judicial System. Only problem is that I know that there is a lesson hidden in it somewhere but cannot think of how! I'm thinking along the lines of expert witnesses giving probability evidence that is then misinterpreted, eg the Sally Clark trial. Has anyone done this? Or have any idea where I can go with this?

3. tango78New commenter

Thanks, I'll have a good readthrough of that article. Ha ha, you never know about the dance approach, could count as Healthy Schools!

4. KarvolOccasional commenter

I cannot remember the exact title of the book that I read this in, but there is something to do with probablities and evidence.
I think the name of the book was "Knowledge Problems: A Intoroduction to Epistemology" or something along those lines. It looked at probabilities to do with what happens when we say we saw something, and what are the real probabilities involved in that. It came under the heading of Gettier problems.
There are also court room scenes in the film "My Cousin Vinny" which look at evidence in a light hearted manner using mathematics.

5. ColinWilson

In the Sally Clark trial it was the expert witness who was misinterpreting the probabilities, the tragety was that no one questioned how Professor Sir Roy Meadows had calculated the probalities in the first case.
Meadows was given a Knighthood his research which ignored conditional probabilities. He cliamed that the probabity of both twins dying from cot death was 1/73000000. But he had arrived at this number by squaring, 1/8500, the probability of a single cot death.
A lesson based on Game Theory looking at 'The Prisoner's Dilemma' might be worth looking into.

6. Maths_MikeNew commenter

Yes a classic where he simply assumed the deaths to be independent - something which even a *** could see to be wrong.

You could be genetically likely to lose children to cot death so the probability of a death given that you already had a previous death is likely to be much lower.

He also coined the
one is unlikely
two is suspicious
and three is murder

I feel so sorry for the women punished as a result of this supposedly intelligent mans stupidity.

How the defense lawyers were unable to discredit his theories is beyond me.

7. tango78New commenter

This all sounds great, I have found a reference to John Moriarty appearing on the BBC's The One Show in January of last year talking about the probability of being called for Jury Service but cannot find the actual clip yet, if I do I will let you all know.
The prisoner's dilemma sounds really good too and could be great with probability trees, it would also be something that would interest the kids!
The 'expert witness' has so many probabilities also, I know that after Sally was cleared the Appeals system was filled with cases who had been convicted on the evidence of an 'expert' witness so there could be more in that.]
Thanks so much for your help so far, any more ideas...

8. ColinWilson

You could try this as a game between pairs over a number of rounds using a payoff matrix. The overall winner is the player with the most points at the end. This has been simulated using computers with different statergies.

9. alabasterNew commenter

this https://www.ncetm.org.uk/resources/20330 resource is really good - examining evidence to work out who the murderer is. What I like is that the maths isn't contrived, working out the percentage of arsenic in different samples to find the samples that match the one found at the murder scene for exanple, actually seems like a real life example of maths being used, rather than made up to give the kids practice. My classes that I have used it with have really enjoyed it.

10. DMNew commenter

I have used this too alabaster and I agree it went down well. I can't agree the maths is not contrived however - poisons were found at all the suspects houses etc - really?!

11. florapost

i'm dargging this out of an old memory - you could maybe get the figure from the sids charity website, but i think i remember them saying that the actual probability of a second cot death in a family given a first is something like 1 in 3000
not that teaching numeracy matters, of course....

12. ColinWilson

There is no such thing as an actual probability in such cases, but this is missing the point. If Bayes Theorem had been understood Sally Clark might still be alive.
The probability that Dover will beat Stevenage in this years FA Cup final might be estimated at 73000000 to 1, it would be unbelievable. But, in the very unlikley event. if they did both reach the final the odds on a Dover win might be around say 5 to 1.
The cot death of twins is very unlikely, murder of young twins by their mother is very unlikely. But both twins died, so one event could be taken as true. Bayers Theorem should have be used to estimate the conditional probability orf murder given that both twins died.

13. tango78New commenter

That looks great, thanks for the tip. How long did it take your classes?

14. tango78New commenter

ooh that's an interesting statistic, if I was feeling brave enough I could even repeat the survey in my class, hmm...

thanks...