Final answer:
The conditional probability that a patient was classified as critical given they died is approximately 66.32%.
Step-by-step explanation:
To determine the conditional probability that a patient was classified as critical given they died, we can use Bayes' theorem. First, let's calculate the overall probability of a patient dying.
The probability of a critical patient dying is 20% (probability of being critical) × 30% (probability of dying given critical) = 0.06 or 6%.
The probability of a serious patient dying is 30% × 10% = 0.03 or 3%.
The probability of a stable patient dying is 50% × 1% = 0.005 or 0.5%.
The total probability of a patient dying is the sum of these probabilities: 6% + 3% + 0.5% = 9.5%.
Now, using Bayes' theorem, we find the probability of a patient being critical given they died:
P(Critical | Died) = (P(Died | Critical) × P(Critical)) / P(Died) = (0.30 × 0.20) / 0.095 = 0.063 / 0.095 ≈ 0.6632 or 66.32%.