Option 1 -> "googled" refers to searching for information online, not necessarily a foolish or futile act.
Option 2 -> "wild-goose chase" is an idiom that specifically means a foolish and hopeless pursuit of something unattainable.
Option 3 -> "frantic search" implies urgency and desperation, but not necessarily foolishness or futility.
Option 4 -> "planned hunt" suggests an organized, deliberate effort, which contradicts the idea of foolishness.
Hence, Option 2: wild-goose chase -> This is an established English idiom that perfectly captures the meaning of a foolish and futile attempt to find or achieve something that is unlikely or impossible to obtain -> correct