Question 7

Events:

  • - Has a certain disease.
  • - A diagnostic test returns positive for the disease.

Probabilities:

  • .
  • .
  • .

Problem: If the test is applied twice, the two test results are independent, and both are positive, what is the (posterior) probability that the selected individual has the disease?

Process: The question can be rephrased to ask what the probability is of a randomly selected person having a certain disease given that the test returned a positive result for the disease twice. This would be the conditional probability .

Answer: 0.9055.