In a study of violent victimization of women and men, Porcerelli et al. collected
information from 679 women and 345 men aged 18 to 64 years at several family practice
centers in the metropolitan Detroit area. Patients filled out a health history questionnaire that included a question about victimization. The following table shows the sample subjects crossclassified by sex and the type of violent victimization reported. The victimization 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.
(a) Suppose we pick a subject at random from this group. What is the probability that this subject will be a woman?
(b) Suppose we picked a man at random. Knowing this information, what is the probability that he experienced abuse from nonpartners?
Now, based on the table we have:-
P(women and partner or multiple victimization)= (34+18)/1024= 52/1024.
P(women)= 679/1024.
P(partner or multiple victimazation)= (44+28)/1024=72/1024.
Now, we have to find certain probabilities.
(1). P(partners or multiple victimization|woman)= P(women and partner or multiple victimization)/P(women).
Thus, we get:-
Required pribability= (52/1024)/(679/1024)= 0.0766
(2). P(woman|partner or multiple victimization)= P(woman and partner or multiple victimization)/ P(partner or multiple victimization).
So, we get:-
Required probability= (52/1024)/(72/1024)= 0.72222
