A team of medical students doing internship have to assist during surgeries at a city hospital The probabilitiies of surgeries rated as very complex, complex, routine simple or very simple are 0.15, 0.20, 0.31, 0.26, 0.08. Find the probabilities that a particular surgery will be rated a) complex or very comples b)neither very complex nor very simple c)routine or complex d) routine or simple

Explanation

Let `E_(1),E_(2),E_(3),E_(4)" and "E_(5)` be the event that surgeries are rated as very complex, complex, routine, simple or very simple, respectively.
`therefore " " P(E_(1))=0.15,P(E_(2))=0.20,P(E_(3))=0.31,P(E_(4))=0.26,P(E_(5))=0.08`
(i) `"(complex or very complex)"=P(E_(1)orE_(2))`
`=P(E_(1)cupE_(2))=P(E_(1))+P(E_(2))-P(E_(1)capE_(2))`
`=0.15+0.20-0[P(E_(1)capE_(2))=0`
`"because all events are independent"]`
`0.35`
(ii) `"(neither very complex nor very simple),"(P(E'_(1)cupE'_(5))=P(E_(1)cupE_(5))`
`=1-P(E_(1)cupE_(5))`
`=1-[P(E_(1))+P(E_(5))]`
`=1-(0.15+0.08)`
`0.77`
(iii) `"P(routine or complex)="P(E_(1)cupE_(2))=P(E_(3))+P(E_(2))`
(iv) `"P(routine or simple)"=P(E_(3)cupE_(4))=P(E_(3))+P(E_(4))`
`=0.31+0.26=0.57`