To find the probability that the patient was initially classified as Level 1 given they are staying overnight, we can use Bayes' theorem.
Let's construct a table with 10,000 hypothetical patients based on the given percentages:
Level | Classification Percentage | Overnight Percentage | Total Patients
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Level 1 | 2% | 99% | 200
Level 2 | 7% | 90% | 700
Level 3 | 30% | 30% | 3000
Level 4 | X% | 10% | X
Level 5 | 10% | 1% | 1000
To find the value of X (percentage of Level 4 patients), we can subtract the percentages of other levels from 100%:
X% = 100% - 2% - 7% - 30% - 10% = 51%
So, there are 5,100 Level 4 patients.
Now, let's calculate the total number of patients staying overnight:
Total overnight patients = (Level 1 overnight patients) + (Level 2 overnight patients) + (Level 3 overnight patients) + (Level 4 overnight patients) + (Level 5 overnight patients)
Total overnight patients = (200 * 99%) + (700 * 90%) + (3000 * 30%) + (5100 * 10%) + (1000 * 1%)
Total overnight patients = 19,800 + 63,000 + 9,000 + 510 + 10
Total overnight patients = 92,320
Now, let's calculate the probability that the patient was initially classified as Level 1 given they are staying overnight:
P(Level 1 GIVEN overnight) = (Number of Level 1 overnight patients) / (Total overnight patients)
P(Level 1 GIVEN overnight) = 200 / 92,320
P(Level 1 GIVEN overnight) ≈ 0.002164
Rounded to three decimal places, the probability that the patient was initially classified as Level 1 given they are staying overnight is approximately 0.002.