## Related questions with answers

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 $45\%$ of the patients are male, $30\%$ of the patients are younger than 30 years of age, $15\%$ of the patients are females older than 30 years of age who are admitted to the hospital, and $21\%$ 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?

Solution

VerifiedSuppose that $x$ is the total number of patients arriving at a hospital emergency room.

$\bullet$ Let us denote as $M,F,Y_{<30},Y_{\ge 30},A$ and $N$ the next events:

$M\,\,\, \rightarrow$ the patient is male ,

$F\,\,\, \rightarrow$ the patient is female ,

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

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

$A\,\,\, \rightarrow$ the patient is admitted to the hospital ,

$N\,\,\, \rightarrow$ the patient is not admitted to the hospital .

Obviously,

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

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