Gary Foshee created a popular probability puzzle that goes like this: "I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"

In this puzzle, knowing that one of Gary's children was born on a Tuesday is as important as knowing that he has one boy. Assuming that having boys and girls are equally likely and that births are equally likely on every day of the week, what is the probability that Gary has two boys, given the available information? (Hint: When Gary said that one is a boy born on a Tuesday, he meant at least one child is a boy born on a Tuesday.)