Question

Hospital records show 12% of all patients are admitted for surgical treatments, 16% are
admitted for obstetrics, and 2% receive both obstetrics and surgical treatment. If a new patient
is admitted to the hospital, what is the probability that the patient will be admitted either for
surgery, obstetrics, or both?

Answer 1

Solution

Let X represent the reason a patient is admitted

Let 'S' be Patients admitted for surgical treatment, 'O' for obstetrics and 'B' for both

$X=\{S, O, B\}$

$S= 12\%$

$O = 16\%$

$B=2\%$

Probability of being admitted for the different reasons:

$P(X=S) = 0.12$

$P(X=O) = 0.16$

$P(X=B) = 0.02$

P(X=S) + P(X=O) - P(X=B)

$= 0.12 + 0.16 - 0.02 = 0.26$

answer: 0.26