Question: In 2010, the puzzle designer Gary Foshee posed this problem: "Mr. Smith has two children, one of whom is a son born on a Tuesday. What is the probability that Mr. Smith has two sons?" Show that there are two different answers to this puzzle, depending on whether Mr. Smith specifi- cally mentioned his son because he was born on a Tuesday or whether he randomly chose a child and reported its gender and birth day of the week.