# A team of medical students doing their internship have to assist during surgeries at a city hospital.The probabilities of surgeries rated as very complex,complex,routine,simple or very simple are respectively 0.15,0.20,0.31,0.26,0.08.Find the probabilities that a particular surgery will be rated complex or very complex

$\begin{array}{1 1}(A)\;0.35\\(B)\;0.45\\(C)\;0.55\\(D)\;0.65\end{array}$

Toolbox:
• $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
Step 1:
Let us denote the surgeries very complex -A,complex -B,routine-C,simple -D,very simple -E
$P(A)=0.15$
$P(B)=0.20$
$P(C)=0.31$
$P(D)=0.26$
$P(E)=0.08$
Where by A,B,C,D & E are mutually exclusive to each other.
Step 2:
$P(B$ or $A)=P(A \cup B)$
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$P(A \cap B)=\phi$
$\Rightarrow P(A)+P(B)$
$\Rightarrow 0.15+0.20$
$\Rightarrow 0.35$
Hence (A) is the correct answer.