Professor Pratorious was visiting his sister, when his young niece, Mary, showed him a list of all the American Presidents in order. As Pratorious looked at the list he mentioned to Mary that of the first five American Presidents, (George Washington, John Adams, Thomas Jefferson, James Madison and James
Monroe,) three died on July 4th. Mary looked at the list and said, "I bet that one of the three was James Monroe." Pratorious was surprised that Mary knew this. Since Mary had no knowledge of how or when James Monroe died, how could she have been so sure he was one of them?

She probably thought that if Monroe was not one of the 3 that died on July 4th then her uncle would have said 3 out of the first 4 died on July 4th. If 3 out of 4 died on July 4th it would seem even more of a coicidence then 3 out of 5.

Since Pratorious stated three of the first five American Presidents died on the fourth of July. Mary knew the fifth must be one of the three or else Pratorious would have said three of the first four. She knew the name of the fifth President by reading it off the list.