The misuse of conditional probability was at its best (worst) in the OJ Simpson murder trial. To give a one-line summary of the context, in June 1994, the American footballer O J Simpson was arrested and charged with the murders of his ex-wife Brown and her friend Goldman.
Against the prosecutor’s argument that Mr Simpson had a history of violence towards his wife, the defence argued that 1 in 2500 of the men who abuse their wives end up murdering them. And the judge seemed to have bought this conditional probability that
P(Husband murders wife | Husband abuses wife) = 1/2500
The real conditional probability should have been
P(Abusive husband is guilty | The wife is murdered)
The probability for this is much higher, close to 80%.
