Lecture 13: Courts and Bayes' Rule

Bayes’ Rule is further discussed in this video in relation to a legal case that demonstrates the importance of correctly understanding conditional probabilities. Miscalculations by prosecutors can have tragic results in situations that are already difficult.
Section 3: Probabilities, Conditioning, and Bayesian Thinking (5/5)
This is the 13th of a total of 40 short videos, which are divided into 11 sections.
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[@robhuntington8504]

At the 3:41 mark when you say 1 out of 1,000,000 would be guilty....are you saying -- out of 1,000,000 mothers with 2 children let's say that 1 of them would kill their 2 children? Actually, not trying to be funny or comment on how likely or not in reality that is. Just want to understand where that figure comes from and what it represents/means.

[@zalida100]

It's just a guess. He's just trying to illustrate that murder of children is such a rare event, so he guesses that the real number, while not quite zero, will be a very small proportion of a population.
i.e. if you have a population of 10 million women parents with 2 children, then perhaps 20 (just a guess) of these women will lose both children. Maybe 10 of these parents murdered their children and the other 10 parents' children died for some other reason.
The accused woman must be included/counted in this group of 20 parents (since she is a parent with 2 dean children).
Without any other evidence, what is the chance that she belongs to the group of parents who murdered their children? Well, that's just saying, out of 20 women, you select one woman. What is the chance that she belongs to one group or the other. The chance is 50/50 that she belongs to one group or the other.
The numbers used are just reasonable guesses and it highlights the very large "error estimate" made by the prosecution in this case. Remember they said that the chance she is not guilty is around 1 in 73 million where the correct estimate is somewhere around 1 chance in 2 or thereabouts.

[@Attoitm]

@@zalida100well was t the death of 2 SIDS 1 in 73m, that should be the number he uses, doesn’t make sense

[@zalida100]

@@Attoitm No, he explained that in order for the 1 in 73 million number to be correct, the 2 events/deaths would have to be independent events. He explained that it's not reasonable to assume that the 2 deaths are independent. 2.10
in the video

[@Attoitm]

@@zalida100 good point, agree