Bad probability calculations show up a lot in the court room. A lot of probability theory is counterintuitive so people can get away with making an intuitive so

Bad probability calculations show up a lot in the court room. A lot of probability theory is counterintuitive so people can get away with making an intuitive sounding argument that is fundamentally wrong. Two high profile cases that I like to bring up are OJ Simpson's murder trial and Sally Clark's trial. I don't remember the exact numbers used in OJ Simpson's trial but the rationalization used is more important than the numbers. His lawyer argued that some very small percentage of men who beat their wives later go on to murder them. Therefore, the fact that OJ beat his wife shouldn't factor into his trial at all. The fundamental flaw in the argument is that there was no question on whether or not his wife was dead. We knew she was dead, so the correct statistic to look at would be, of women who were beaten by their husbands and later murdered, how often was the husband the murderer? And the answer was some large percentage, like more than 90%. Sally Clark's case was even sadder. She was eventually released from prison but committed suicide not long after. She was on trial for murder after her second child died from SIDS, her first child having died the same way. The prosecution brought in an "expert witness" to give the probability of one woman having two children die from SIDS. All he did was take the incidence of SIDS at the time, 1 in 8500, and square it, coming up with 1 in 75 million. No other evidence of murder was found, she was convicted because of the statistical argument. This argument has multiple flaws. It assumes that the two incidences of SIDS in this case were independent events, which is not necessarily the case. On top of that, even if you could assume they were independent events, a 1 in 75 million event doesn't mean the event is impossible. A person should not be convicted on that probability alone with no other evidence.