Jo has a test for a nasty disease. We denote Jo's state of health by the variable a and the test result by b.
The result of the test is either ‘positive' (b = 1) or ‘negative' (b = 0); the test is 95% reliable: in 95% of cases of people who really have the disease, a positive result is returned, and in 95% of cases of people who do not have the disease, a negative result is obtained. The final piece of background information is that 1% of people of Jo's age and background have the disease.
OK - Jo has the test, and the result is positive. What is the probability that Jo has the disease?