Wonderful! If only children were taught to think like this in schools, instead of memorizing and repeating certain "facts" (many of which aren't facts at all) and adopting mainstream ideas. Thank you!
The teaching of statistics and logic such as this should be made compulsory for all children. They would then be able to see through the lies of the grown-ups and the authorities, with their malevolent intentions. But they won't make it compulsory, because the children would then be able to see through the lies of the grown-ups and the authorities, with their malevolent intentions.
At 2:51 I'm struggling to understand why P(Evidence | Innocence) isn't just equal to P(Evidence). I don't get the difference between them. If 1 in 100 people wear size 13, then P(Evidence) = 1/100, no?
Because the reason for the analysis is to determine someone’s innocence beyond a reasonable doubt. They call it conditional probability, and you need to clearly state the two conditions being analyzed in relation to one another-the premise of innocence (condition B) & the finding of the evidence in question (condition A). Because prosecutors and defense attorneys try to establish reasonable doubt with use, and misuse, of statistics, wording it this way (“probability of evidence, given innocence” as opposed to the other way around) is also to highlight the important difference between this question and the other question that prosecutors fallaciously use: “probability of innocence” given this “evidence”, which we cannot know because probability of innocence is dependent on so many other factors as well. In other words, the wording puts the term “innocence” clearly where it belongs, emphasizing that there is no way to make a claim of the probability of innocence with the limited information given. Hope that helps.
I was about to comment that there is a much easier way to understand this situation when suddenly he gave us the answer in the last 20 seconds: He calls it Bayes theorem, but the bottom line is that you need to know your base rates. Tomato, Tomahto. . . . In any small town there will be will be at least 100 people with size 13vshors and in even a small city there will be a few hundred more.
Still, there's a high chance that there is more than 1 person that matches the foot size, because when the sample size is not enough big (there is a name to this fact, but I can't remember it) the probability can vary. For example, imagine 1 of 10 men have earrings. If you randomly ask 10 men if they have earrings on, it's really high likely that no one will have earrings on, but if you ask 1 million men, then about 100.000 (it won't vary that much) will tell you they have earrings on. Also, for this to work, it has to be a highly precise statistic (so it obviously can't be made up like some court cases). So, short answer, you can't convict someone for this, and the P(Evidence) should be pretty higher, varying thanks to the small sample size (I don't study probability so I don't know any formula to calculate it, but it should vary a lot if you think about it).
That is all in absence of confounding factors. The killer might have been wearing a size 13 shoe on a size 12 foot or 11 foot or had one 13 and one 12 foot or was a homeless person wearing the only shoes he could find or someone with a size 13 foot stepped on the victim without noticing as they were pushed along by the crowd. There is also the possibility that due to the nature of the crowd involved people who have size 13 feet may have come together either due to like mindedness or deliberately as a size 13 foot club and therefore all those present had size 13 feet. Random statistics should never be used to claim something is in fact random or unlikely to have another explanation. About the only thing random statistics are actually good for is determining if you should stock five widgets for the Christmas rush or a thousand widgets on average both choices will be wrong.
Calling this the Prosecutor's Fallacy just seems like a fancy name for flawed logic. Giving something a name as a way to say it's true is often used to justify something. Talking about "woke" society is an example of this. Another example of flawed logic, or "false logic" is saying that a person having "means, motive and opportunity" indicates a person is guilty. Means and opportunity are dependent on each other because because if you have a hand gun but you aren't in the vicinity you don't have means to shoot someone and if you are next to the victim but unarmed you don't have opportunity to shoot. As for motive, people ranging from the homeless to billionaires tend to want more than they have but most people don't act on it in a criminal manner. Having means, motive and opportunity is at best reason to consider someone as a possible suspect, but police and prosecutors will decide someone is guilty first then treat it as evidence.
