A Tuesday Quiz

I recently wrote two pieces about the puzzle relating to sons born on a Tuesday: A Son born on Tuesday and Sons and Tuesdays. I also posted a beautiful essay on the subject by Peter Winkler: Conditional Probability and “He Said, She Said”. Here is the problem:

You run into an old friend. He has two children, but you do not know what their gender is. He says, “I have a son born on a Tuesday.” What is the probability that his second child is also a son?

A side note. My son Alexey explained to me that I made an English mistake in the problem in those previous posts. It is better to say “born on a Tuesday” than “born on Tuesday.” I apologize.

Despite this error, I was gratified to hear from a number of people who told me that I had converted them from their solution to my solution. To ensure that the conversion is substantial, I’ve created a new version of the puzzle on which my readers can test out their new-found understanding. Here it is:

You run into an old friend. He has two children, but you do not know what their gender is. He says, “I have a son born on a Tuesday.” What is the probability that his second child is born on a Wednesday?

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