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Stat 110 Student Reassures Girlfriend Positive STD Result Likely Statistical Anomaly

Madison attempting, in vain, to interpret the data presented to him.
CAMBRIDGE, MA--After a positive result on a pair of self-administered tests for an STD, Leverett junior Werther Madison was seen reassuring his girlfriend that despite these results, the probability that he cheated on her remains counterintuitively low. Madison, a student of the popular course Statistics 110: Introduction to Probability, sought to interpret these results using the same techniques he learned in Stat 110.
“I do admit that a positive test result does increase the likelihood that we have the disease, but not by nearly as much as you might think,” said Madison. “The chance we have the disease is still proportional to the prior probability that I would cheat and bring an STD into our relationship. Which is like zero, since I would never--wait, don’t leave!”
Despite his best efforts, his argument seemed only to make the situation exponentially worse, and Madison found it increasingly difficult to remember relevant details from his statistics course.
“There’s a limit to how bad this can be, right? Let’s assume the number of STDs I’ve brought into our relationship follows a Poisson distribution. I can assure you my lambda is tiny. Miniscule! Two at most.”
After the conversation, Madison updated his probability of still having a girlfriend to accommodate for his newest observations. Madison could be seen today sitting, dejected, in his statistics final, getting firsthand experience with the principle of inclusion-exclusion.
© 2016