Solution:
First some terminology:
- Specificity is the probability that the test results are negative for a person that does not have the disease.
- Sensitivity is the probability that the test results are positive for a person that does have the disease.
- Predictive Value Negative is the probability that a person does not actually have the disease if this person’s results for the test are negative.
- False Positive is the probability that a person who does not have the disease will get positive test results. In this case, the false positive rate is 10 %.
- False Negative is the probability that a person who does have the disease will get negative test results. In this case, the false negative rate is 20 %.
- To find these rates it is helpful to draw
a tree diagram:
- This is an application of Bayes’
Rule, a theorem of probability, which can be used to revise the
probability a patient does or does not have the disease based on
additional information being introduced ... in this case, a
positive or negative result on a this test.
If the test results are negative, then there is now a 98 % chance that the woman does not actually have the disease. This is a revision of the original probabilities based on the information given by the test.
