Final answer:
Twain is trying to communicate the role of chance and deception in human interactions in the story.
Step-by-step explanation:
The second-layer idea that Twain is trying to communicate with the story "The Celebrated Jumping Frog" is b) The role of chance and deception in human interactions. Throughout the story, Twain presents the theme of deception and how it can often lead to unexpected outcomes. The main character, Jim Smiley, is deceived by another character who replaces his winning frog with a different frog, highlighting how chance and deception can affect human interactions.