Former pro football star O. J. Simpson was accused of murdering his wife. In the trial, a defense attorney pointed out that although Simpson had been guilty of earlier spousal abuse, annually only about 40 women are murdered per 100,000 incidents of partner abuse. This means that P(murdered by partner | partner abuse) = 40/100,000. More relevant, however, is P(murdered by partner| partner abuse and women murdered). Every year it is estimated that 5 of every 100,000 women in the United States who suffer partner abuse are killed by someone other than their partner (Gigerenzer, 2002, p. 144). Part of a tree diagram is shown starting with 100,000 women who suffer partner abuse.

a. Based on the results stated, explain why the numbers 45 and 5 are entered as shown on two of the branches.
b. Fill in the two blanks shown in the tree diagram.
c. Conditional on partner abuse and the woman being murdered (by someone), explain why the probability the woman was murdered by her partner is 40/45. Why is this so dramatically different from P(murdered by partner | partner abuse) = 40/100,000?

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Murdered Murdered by Partner Yes Yes (45) No (5) 100,000 Women who suffer partner abuse