Even seasoned complex-systems scientists struggle with problems in probability theory. This is because the human brain isn't very well suited to deal with probabilities. In the first part of the talk I will discuss different interpretations of probability (classical, frequentist, subjective), and the philosophy surrounding these interpretations.
In the second part I will talk about some paradoxes in probability theory, at a level suitable for masters students and PhD students. Some of these paradoxes will be familiar to most of you, for example the Monty Hall problem. But do you know how Simpson's paradox may influence what medicine you take? Are you familiar with the Tuesday paradox or the prosecutor's fallacy, or the fallacy of the defense lawyer ? Do you understand why obesity can seem to make people live longer if they have a heart condition? What's the probability that the Sun will rise tomorrow? Do you know why the sequence HHT is likely to come before HTH when you keep flipping a coin? If you don't, come to the talk. I will also discuss the Sally Clark case, a women convicted in of murdering her two children in 1999 in the UK, based on blatantly incorrect probability arguments. Another case involves Lucy Letby, a former nurse, convicted in 2023, and currently serving fourteen life sentences for murdering children in a hospital in England. In her case too, the statistical evidence has come under scrutiny, and an appeal process is in progress.
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