Thomas Bayes and O.J. Simpson

After posting about The Prosecutor’s Fallacy I recalled a similar case with the Defense in the O.J. Simpson trial. The issue was summarized in What is your favorite problem for an introduction to probability?:

… one of Simpson’s lawyers, Alan Dershowitz, noted that even though Simpson beat
his wife, that hardly mattered, because in the United States, four million women are
battered every year by their male partners, yet only one in 2,500 is ultimately
murdered by her partner (1 in 1000), so, by the ‘reasonable doubt’ criterion, this is
irrelevant. The jury found that argument persuasive, but it’s spurious. The relevant
question was what percentage of all battered women who are murdered are killed by
their abusers, which ain’t 1 in 1000, but rather 9 in 10.

For a clear explanation of the details see Chances Are, by Steven Strogatz, which is reprinted in his excellent book, The Joy of x: A Guided Tour of Math, from One to Infinity.

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