\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider a rare disease that affects approximately 1 in every 1,000 people. A medical test developed for detecting this disease has the following characteristics:
  • Sensitivity: If a person has the disease, the test correctly returns a positive result 99\(\pourcent\) of the time.
  • Specificity: If a person does not have the disease, the test correctly returns a negative result 95\(\pourcent\) of the time.
Find the probability in percent that a person actually has the disease if their test result is positive (round to 1 decimal place):
\(\PCond{\text{Disease}}{\text{Test positive}} = \)
\(\pourcent\)