In 1994, O. Simpson, an actor and former professional American football player, was accused of murdering his ex-wife, Nicole Brown Simpson. News of...

1.     In 1994, O. J. Simpson, an actor and former professional American football player, was accused of murdering his ex-wife, Nicole Brown Simpson. News of this court case filled the media for months. During the trial, Alan Dershowitz, an advisor to Simpson's defence attorneys, claimed that Simpson's previous accusation of spousal abuse was not particularly relevant. The evidence was that only about one in 2500 men who batter their significant others (wives, girlfriends) go on to kill them.  This statement went unchallenged at the trial, but was subsequently corrected in a letter to the editor in Nature in 1995. In 1994, there were approximately 125,000,000 women in the USA. That year there were approximately 3,500,000 women who were battered. There were approximately 5,000 women murdered. Approximately 1,400 women were murdered by the man who battered them.

a)     What is the probability that a woman was battered in 1994?

b)    What is the probability that a woman was murdered in 1994?

c)     The defence argued that the probability of a woman being murdered by her batterer, given she was battered was 1 in 2,500, so the fact that O.J. Simpson battered his wife was irrelevant. The prosecution should have challenged this probability because what was at issue was that Nicole Brown was murdered. Use Bayes Rule to calculate the probability that she was murdered by her batterer, given that she was murdered.