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Question

In a study of patients arriving at a hospital emergency room, the gender of the patients is considered, together with whether the patients are younger or older than 30 years of age, and whether or not the patients are admitted to the hospital. It is found that 45%45\% of the patients are male, 30%30\% of the patients are younger than 30 years of age, 15%15\% of the patients are females older than 30 years of age who are admitted to the hospital, and 21%21\% of the patients are females younger than 30 years of age. What proportion of the patients are females older than 30 years of age who are not admitted to the hospital?

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Suppose that xx is the total number of patients arriving at a hospital emergency room.

\bullet Let us denote as M,F,Y<30,Y30,AM,F,Y_{<30},Y_{\ge 30},A and NN the next events:

MM\,\,\, \rightarrow the patient is male ,

FF\,\,\, \rightarrow the patient is female ,

Y<30Y_{<30}\,\,\, \rightarrow the patient is younger than 30 years of age ,

Y30Y_{\ge 30}\,\,\, \rightarrow the patient is older than 30 years of age ,

AA\,\,\, \rightarrow the patient is admitted to the hospital ,

NN\,\,\, \rightarrow the patient is not admitted to the hospital .

Obviously,

F=M,Y30=Y<30,N=A.F=M^{'} , \,\,\,\,\,Y_{\ge 30}={Y_{<30}}^{'} ,\,\,\,\,\, N=A{'}.

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