A patient gets tested for a disease. The test is 90% reliable (that is P(testing positive│have disease)=.9 . 2% of the population has this disease. The test gives a false positive 5% of the time (that is P(testing positive│NOT diseased)=.05). What is the probability that the patient has the disease given that she tested positive?

Question

A patient gets tested for a disease.  The test is 90% reliable (that is P(testing positive│have disease)=.9 .  2% of the population has this disease.  The test gives a false positive 5% of the time (that is P(testing positive│NOT diseased)=.05).  What is the probability that the patient has the disease given that she tested positive?