Two girls – the value of information

We came across the ‘two girls’ version of the children's gender problem nearly 35 years ago. How we came to it we cannot remember, but Martin Gardner had published a variant of it in the Scientific American in 1959. It re-emerged for us in the summer of 2010, following the publication of an article in Science News [1]. Subsequently Keith Devlin wrote about how this re-emergence impacted on him, and noting that ‘Probability Can Bite“ [2]. The mathematics herein reflects and extends that in Devlin's article.In case the reader has not encountered the problem before, we first pose four problems.1. A family has two children. One of them is a girl. What is the probability that they are both girls?2. A family has two children. The younger is a girl. What is the probability that they are both girls?3. A family has two children. One of them is a girl, and she was born on a Tuesday. What is the probability that they are both girls?4. A family has two children. One of them is a girl, and she has green hair. What is the probability that they are both girls?