Question

Exercise 2 (SOA type and COVID related). Upon arrival at a hospital's emergency room, patience are categorized according to their con- dition: critical, scrious and stable. In the past year, 20% of emergency room patients were critical, 40% of them were serious and the rest stable. Moreover, 50% of critical patients died, 20% of serious patients died and 1% of the stable patients died. Given that a patient survived, what is the probability they were categorized as serious?

Answer 1

Solution:- Let A. Patient is critical Az & Patient is serious Azi Patientsis stable, and E & Person died E Person Swenne er Patients died given? PLA) = 0.2 P(A2) = 0.4 PLA3) = 0.4 PLE/A) = o.s → PLEA) = 0.5 PLE/A2) = 0.2 >PLELA2=0.8 PLE/A3)=0:01 PLE/A3) = 0.99 or patients survive + Hore we lese baye's theoren because A PLA) + Plaz) + P(A3) = 0.2 +0.4+0.42 According to Baye's throuon, Patient Swwne , Probability that they were categorised as Seniows üs PLA2 LE') P/A2) Pl ElA Plast plEHAT) +play)ple IA, JAPAJALEHA)

PLAZLE') 0.4x08 10.2x0.5)+ lo.4x0.8) + LO.4x0.99 0.32 Oil of 0.32 + 0.996 0.32 => 0.32 O 33 +0.396 0.726 +004402 therefore, P (A2/E') = 0.4408 راه