It is a fairly common mistake to confuse "either/or" and "fifty-fifty." But just because you either have the disease or don't, the probabilities are not fifty-fifty. You need to factor in how common the disease is and the accuracy of the test.

Remember Andy Rooney's 50-50-90 rule: "Any time you have a fifty-fifty chance to get something right, there is a 90% probability you'll get it wrong!"