During the O. Simpson trial the prosecution argued that the history of domestic abuse by O. towards his ex-wife Nicole Brown showed a pattern of...

During the O.J. Simpson trial the prosecution argued that the history of domestic abuse by O.J. towards his ex-wife Nicole Brown showed a pattern of escalating violence which culminated in her murder. To make the point the chief prosecutor famously used the line "A slap is a prelude to homicide". Predictably, the defense argued this history of domestic abuse meant nothing. The defense used the following statistics to make their argument: over 4 million women were victims of domestic abuse in 1992 and only 1,432 of these were killed by their significant others. Therefore the probability, in 1992, that an abuser murders their spouse is less than 1/2500. Therefore, they argued that very few wife beaters actually go on to murder their wives.

In your post you will refute the defense's argument using probability theory. Here is a guide to the argument:

(a) Write the defense's statistic in terms of a conditional probability where M is the event that the

women is murdered by their abuser, and A is the event that they were previously abused.

(b) What key piece of information is the defense conveniently forgetting to condition on? Hint: Is it

relevant to consider the probability that O.J. will murder Nicole at some future date?

(c) If I told you that 90% of the time when an abused women is murdered, the murderer was the

abuser (this is true). How would you respond to the defenses argument?