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A new disease "slideclosis" has taken hold among business students all over the world and affects 3% of those students. It seems to be related to overexposure to slides in classes, and the symptoms consist of complete disengagement from the class accompanied by the affected students' eyes getting stuck on the computer screen before them, occasional random chuckling or hitting the neighbour to draw their attention to the screen. Because these symptoms are indistinguishable from typical student behaviours caused e.g., by looking at facebook or tumblr during class, a special test was designed to establish whether the symptoms are indeed caused by slidecosis. The test accurately identifies existing slidecosis in 89% of the cases, and it produces 6% false positive in students who don't have actually the disease. Your professor fears that your class has a particularly high prevalence of slidecosis and has all of you tested. The test result for the person to your left came back positive. Luckily, you personally are not affected by the disease and can calculate the probability that your neighbour actually has the disease. Define appropriate events and demonstrate the calculation of probabilities of interest in terms of formulas with detailed steps.

(a) Which concept is most appropriately used to complete the calculations?

(b) What is the probability that your neighbour has the disease knowing that the test was positive?

(c) The person behind you tested negative for the disease. What is the probability that the person has the disease despite a negative test?