We obtain the marginal probability P(E) by adding these four joint probabilities as follows: P(E) = P(En A) + P(En B) + P(E n C) + P(En D) 3.5 Bayes' T ap abe = .0881 +.0597 +.1289 +.1667 =.4434 ne re: The result, as expected, is the same as the one obtained by using the marginal tot ia as the numerator and the total number of subjects as the denominator. llideda Exercises 3.4.1 In a study of violent victimization of women and men, Porcerelli et al. (A-2) collected information from 679 women and 345 men aged 18-64 years at several family practice centers in the metropolitan Detroit area. Patients filled out a health history questionnai that included a question about victimization. The following table shows the sample suk jects cross-classified by sex and the type of violent victimization reported. The victimiza. tion categories are defined as no victimization, partner victimization (and not by others) victimization by persons other than partners (friends, family members, or strangers), and those who reported multiple victimization. No Multiple Victimization Victimization Partners Nonpartners Total Women 611 34 16 679 18 3.4. Men 308 10 345 17 10 Total 919 44 1024 33 28 Source: Data provided courtesy of John H. Porcerelli, Ph.D., Rosemary Cogan, Ph.D. 3.4 (a) Suppose we pick a subject at random from this group. What is the probability this subject will be a woman? (b) What do we call the probability calculated in part a? 3. (c) Show how to calculate the probability asked for in part a by two additional methods (d) If we pick a subject at random, what is the probability that the subject will be a woman and have experienced partner abuse? (e) What do we call the probability calculated in part d? (f) Suppose we picked a man at random. Knowing this information, what is the proba- bility that he experienced abuse from nonpartners? (g) What do we call the probability calculated in part f? (h) Suppose we pick a subject at random. What is the probability that it is a man or someone who experienced abuse from a partner? (i) What do we call the method by which you obtained the probability in part n

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