Let,
X1 = Patient that is Critical
X2 = Patient that is Serious
X3 = Patient that is Stable
D = Dead Patient
V = Survived Patient
Using Baye's Formula:
Let,
P(X2, V) = the probability that the patient who survived was categorized as serious upon arrival.
We are given,
P(X1) = 0.12
P(X2) = 0.27
P(X3) = 1 - (0.12 + 0.27) = 0.61
P(X1,V) = 1 - P(X1,D) = 1 - 0.43 = 0.57
P(X2,V) = 1 - P(X2,D) = 1 - 0.26 = 0.74
P(X3,V) = 1 - P(X3,D) = 1 - .05 = 0.95
We now solve for the probability that the patient who survived was categorized as serious upon arrival,
The probability that the patient who survived was categorized as serious upon arrival is 0.2357.