Many of you are familiar with the old Monty Hall problem. You might also be aware that it rose to prominence as a result of a column in Parade magazine by Marilyn vos Savant. After Savant’s initial discussion of the problem, she received a flood of angry letters, some from actual mathematicians, saying that she was wrong and that her answer was foolish. Actually, Savant got it right, and the problem is now a staple of courses in elementary probability theory.
I recently got it into my head to track down the actual correspondence she received on the issue. Courtesy of the local public library, I found an anthology of some of the letters she received during the time she wrote the column. The Monty Hall discussion was in there, as I hoped.
To my surprise, however, I discovered a second probability puzzle that she addressed that also led to some heated controversy in the replies. It’s a classic puzzle, so perhaps you have heard it before. But just in case you haven’t, here it is:
A shopkeeper says she has two new baby beagles to show you, but she doesn’t know whether they’re both male, both female, or one of each. You tell her that you want only a male, and she telephones the fellow who’s giving them a bath. “Is at least one a male?” she asks him. She receives a reply. “Yes!” she informs you with a smile. What is the probability that the other one is a male?
Feel free to hash that out in the comments.