Problem 1: A patient is tested for a virus, V. The accuracy of the test is 98%. This virus, V, is currently present in 4 out of 100 people in the region the patient lives in:
a) What is the probability that a patient having the virus, V, if they test positive?
b) What is the probability of a patient still having the virus if the result of the test is negative?
Problem 2: Apart from assessing whether patients are suffering from the virus, V (in Problem 1), by using the test, a doctor usually also checks for other symptoms. According to a doctor, about 85% of patients with symptoms such as fever, nausea, abdominal discomfort, and malaise have the virus, V:
a) What is the probability of a patient having the virus, V, if they have the symptoms mentioned previously and their test result for the virus is positive?
b) How likely is it that the patient has the virus if they have the symptoms mentioned previously, but the result of the test is negative?
Problem 3: On a certain island, one in two...