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Originally Posted by aigel
I notice that sometimes bad events pile up - almost like there is a correlation - but it is just like rolling the same number 3 times in a row throwing dice. It happens ...
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This comment reminded me of independent events fallacy. Multiple rolls of a die are alway independent events. However, bad events in life can trigger others. If you get divorced, this may impact your emotional state or work performance, and are now much more likely to get a DWI or get fired from work, for example.
The famous example of this was the Sally Clark baby murder case. Two of her babies died in the crib.
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The case was widely criticised because of the way statistical evidence was misrepresented ....an expert witness that "one sudden infant death in a family is a tragedy, two is suspicious and three is murder unless proven otherwise" (Meadow's law). ...the probability of a single cot death was 1 in 8,543, so the probability of two cot deaths in the same family was around "1 in 73 million" (8543 × 8543). First, Meadow's calculation was based on the assumption that two SIDS deaths in the same family are independent. The RSS argued that "there are very strong reasons for supposing that the assumption is false. There may well be unknown genetic or environmental factors that predispose families to SIDS, so that a second case within the family becomes much more likely than would be a case in another, apparently similar, family."[17] The prosecution did not provide any evidence to support its different assumption.[17] In a 2004 article in Paediatric and Perinatal Epidemiology, Professor of Mathematics Ray Hill of Salford University concluded, using extensive SIDS statistics for England, that "after a first cot death the chances of a second become greatly increased", by a dependency factor of between 5 and 10.[18]
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Another famous example was Feynman's analysis of the Space Shuttle explosion. The odds of one o-ring failing are small. But, if one does fail, the odds of the others failing are now much higher. Chain reaction.