If a student randomly guesses on a true false test, what is the probability that the student guesses at least 8 out of 10 correct? Before you get excited and start thinking of a Binomial(10, 0.5), listen to this SciAm 60 Second Science podcast. Researchers from Northwestern University published an article in Nature Neuroscience (key figure below), which indicates that “guesses” can be more accurate than educated responses. Investigator Dr. Ken Paller, professor of psychology at Northwestern says:
“Remarkably, people were more accurate… when they had been distracted than when they had paid full attention. They also were more accurate when they claimed to be guessing than when they registered some familiarity for the image.”
Read more. I am teaching stochastic processes this semester, and may have to work this research into an example. Of course, I might end up inviting trouble with, um, creative homework solutions, but how things really work can be fun in class.
The moral of the story: be intuitive.
Behavioral and ERP results from the Nature Neuroscience paper
Punk Rock Operations Research 
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