A hospital uses the Emergency Severity Index1 to classify its patients. This classification scheme has five categories from Level 1 (the patient requires resuscitation or other highly emergent care) to Level 5 (the patient requires non-urgent care).

Question

At this hospital, 2% of patients are classified as Level 1, 7% are classified as Level 2, 30% are classified as Level 3, 10% are classified as Level 5, and the remaining percentage of patients are classified as Level 4. At this hospital, 99% of Level 1 patients stay overnight, 90% of Level 2 patients stay overnight, 30% of Level 3 patients stay overnight, 10% of Level 4 patients stay overnight, and 1% of Level 5 patients stay overnight.
Kennedy (a nurse at this hospital) randomly selects a patient who is staying in the hospital overnight. What is the probability that this patient was initially classified as Level 1? Round to the three decimal places.

Hint: Construct a table with 10,000 hypothetical patients.

P(Level 1 GIVEN overnight) =

Answer 1

First, let's calculate the total number of patients staying overnight by summing the percentages of each level that stay overnight:
(2% of Level 1) + (90% of Level 2) + (30% of Level 3) + (10% of Level 4) + (1% of Level 5) = 2% + 90% + 30% + 10% + 1% = 133% (since 133% is the total, we can add in the remaining percentage of patients classified as Level 4 that stay overnight)

Next, we need to determine the percentage of overnight patients that are initially classified as Level 1. To do this, we divide the percentage of Level 1 patients by the total number of patients staying overnight:
(2% of Level 1) / (133% total overnight patients) = 2% / 133% = 0.015 (rounded to 3 decimal places)

Therefore, the probability that the patient Kennedy randomly selected was initially classified as Level 1 is 0.015.