Suppose you are a nurse screening a set of students for a sickness called Diseasitis.
- You know, from past population studies, that around 20% of the students will have Diseasitis at this time of year.
You are testing for Diseasitis using a color-changing tongue depressor, which usually turns black if the student has Diseasitis.
- Among patients with Diseasitis, 90% turn the tongue depressor black.
- However, the tongue depressor is not perfect, and also turns black 30% of the time for healthy students.
One of your students comes into the office, takes the test, and turns the tongue depressor black. What is the probability that they have Diseasitis?