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, .08. Find the probabilities that a particular surgery will be rated.
(a) routine or complex
(b) routine or simple
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, .08. Find the probabilities that a particular surgery will be rated.
(a) routine or complex
(b) routine or simple

Solution:
Let’ say
Event that surgeries are rated as very complex =E_{1}
Event that surgeries are rated as complex =\mathrm{E}_{2}
Event that surgeries are rated as routine =\mathrm{E}_{3}
Event that surgeries are rated as simple =\mathrm{E}_{4}
Event that surgeries are rated as very simple =E_{5}
Given that P\left(E_{1}\right)=0.15, P\left(E_{2}\right)=0.20, P\left(E_{3}\right)=0.31, P\left(E_{4}\right)=0.26, P\left(E_{5}\right)=0.08
(a) P (routine or complex) =P\left(E_{3} \cup E_{2}\right)
=P\left(E_{3}\right)+P\left(E_{2}\right)-P\left(E_{3} \cap E_{2}\right)
[\because By General Addition Rule]
=0.31+0.20-0 [given ]
=0.51
(b) P (routine or simple) =P\left(E_{3} \cup E_{4}\right)
=P\left(E_{3}\right)+P\left(E_{4}\right)-P\left(E_{3} \cap E_{4}\right)
[\because By the General Addition Rule]
=0.31+0.26-0 [as given ]
=0.57