Because a new medical procedure has been shown to be effective in the early detection of an illness, a medical screening of the population is proposed. The probability that the test correctly identifies someone with the illness as positive is 0.99, and the probability that the test correctly identifies someone without the illness as negative is 0.95.
The incidence of the illness in the general population is 0.0001. You take the test, and the result is positive. What is the probability that you have the illness?