Numpty >>
sunday june 18 - 13:00, Edited
sunday june 18 - 13:19 In my experience a lot of so-called experts make flaws when calculating probabilities. This is usually because their expertise is in another field and not in mathematics.
For instance, a medical expert decides that the probability of an infant dying in unusual circumstances is 1 in a million. This is a tragedy but not necessarily suspicious. 4 young children in the same family die in similar circumstances and the medical expert tells the courts that this is evidence that at least one of the parents is guilty of murder. The calculation that he does is 1 in (1 million )^4 = 10^24, which assumes that the deaths have no medical connection. The courts believe the expert witness and the mother is found guilty.
However, if the 4 children all had the same undiagnosed syndrome that was inherited from their parents then the deaths are related. Let's say the medical expert was correct about 1 in a million for the first child. But it's entirely possible that the chance of subsequent children inheriting the same genes from their parents is (say) 1/4, given that the first child already had it. In which case the calculation that the 3 subsequent children all have the same syndrome as the first one is 1 in 4^3 = 1 in 64.
And all 4 children having exactly the same syndrome is = 1 in 64 million. It's a tragedy but not a crime.
As for the 'expert witness' it's not his medical knowledge that was flawed, just his mathematical reasoning.
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However, in this case the poster is claiming to be an expert mathematician and I'm looking forward to a well-reasoned answer.
I can only do beginners' maths, so if there are any complicated equations I'll have to get @Siege to help out.