Suppose there is a test for esophageal cancer that is 95% accurate both on those that do and those that do not have esophageal cancer. if 0.7 percent of the population has esophageal cancer, compute the probability that a person has this cancer, given that his or her test results indicates so.
It was already stated that the probability that the population may have esophageal cancer is 0.7 percent. However, the additional statement that the accuracy is 95% will affect the probability as follows:
Probability = (0.007)(0.95) = 0.00665 or 0.665%
So instead of 0.7%, the probability will decreased to 0.665% because of the accuracy.
