[math-fun] Schroedinger's daughter

OK, I thought that I understood this, but here's a variation: A friend writes a girl's name on a piece of paper and puts it (unopened) in your pocket. A random parent of two children comes up to you and says, "I have a daughter named Mary." At this point, the probability that Mary's sibling is a girl is 1/3 (I think). However, if you look at the piece of paper, and it says "Mary", the probability changes to 1/2 (approximately). Is this correct? Bill C.