During the murder trial of O. J. Simpson, Alan Der-showitz, an advisor to the defense team, stated on television that only about 0.1% of men who batter their wives actuallymurder them. Statistician I. J. Good observed that even if, given that a husband is a batterer, the probability he is guilty of mur-dering his wife is 0.001, what we really want to know is the probability that the husband is guilty, given that the wife wasmurdered. Good estimates the probability of a battered wifebeing murdered, given that her husband is not guilty, as 0.001.The probability that she is murdered if her husband is guiltyis 1, of course. Using these numbers and Dershowitz’s 0.001probability of the husband being guilty, find the probabilitythat the husband is guilty, given that the wife was murdered.Source: Nature.

College Algebra
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ISBN:9781337282291
Author:Ron Larson
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Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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During the murder trial of O. J. Simpson, Alan Der-
showitz, an advisor to the defense team, stated on television

that only about 0.1% of men who batter their wives actually
murder them. Statistician I. J. Good observed that even if, given

that a husband is a batterer, the probability he is guilty of mur-
dering his wife is 0.001, what we really want to know is the

probability that the husband is guilty, given that the wife was
murdered. Good estimates the probability of a battered wife
being murdered, given that her husband is not guilty, as 0.001.
The probability that she is murdered if her husband is guilty
is 1, of course. Using these numbers and Dershowitz’s 0.001
probability of the husband being guilty, find the probability
that the husband is guilty, given that the wife was murdered.
Source: Nature.

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