92% of undergrads, and even 83% of grad students who had taken advanced courses in probabilities and statistics didn't know the first thing about probabilities.

If you're wondering how illogical the human race is, this is one interesting piece of evidence. We apparently did not evolve to think logically (altho if you read the comments, some are arguing that the illogical answers had some type of logic to them). 
Thankfully there are some humans who can think better than us. One of them, Eliezer Yudkowsky, writes this really extremely interesting blog called LessWrong. 
Check out this post he has on the Conjunction Fallacy.
He also has some really good explanations of quantum mechanics which I've never seen elsewhere.