At the end of Monday's IRC, flagamuffin and wasoxygen were briefly discussing http://crackthesenuts.blogspot.com/2013/12/born-on-tuesday.html I really love these problems and wanted to discuss, but I missed you guys.

The question was: "Suppose I tell you that I have two children and one of them is a boy, what is the probability that I have two boys?" He claims the answer is 1/3, but I think it depends on why he is telling us that he has a boy.

If he was thinking of one of his children, and told us the gender of that child, we have no information on the other child, and the probability remains at 1/2. If instead we had asked "Do you have at least one boy?", and he replied "Yes", the probability is 1/3 that he has two.

The lecture in the link goes over some similar problems, and provides a framework for dealing with them. He uses it to explore some pretty interesting questions, like the probability of humanity lasting another ten thousand years.