Via Marginal Revolution, the "girl named Florida" problem.
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I've been reading Leonard Mlodinow's The Drunkard's Walk: How Randomness Rules our Lives. The book covers the Monty Hall problem, Bayes's Theorem, availability bias, the illusion of control and so forth. If these are unfamiliar, look no further for an entertaining account.
On the other hand, I can't say that I learned much I didn't already know. Nevertheless, I still enjoyed reading the book - it's well written and filled with interesting nuggets (Did you know that the great mathematician Paul Erdos refused to believe that you should switch doors?). If you teach probability theory or intro stats you will find lots of good examples to brighten up your lectures.
One problem did intrigue me. Suppose that a family has two children. What is the probability that both are girls? Ok, easy. Probability of a girl is one half, probabilities are independent thus probability of two girls is 1/2*1/2=1/4.
Now what is the probability of having two girls if at least one of the children is a girl? A little bit harder. Temptation is to say that if one is a girl the probability of the other being a girl is 1/2 so the answer is 1/2.