Explanation:

- Correct Answer: Option 4: Futile search

- A "wild goose chase" refers to a futile search or a pointless endeavor, where the effort will likely lead nowhere.

- Option 1: Doing something crazy

- This means engaging in irrational or unpredictable behavior, unrelated to the "wild goose chase" idiom.

- Option 2: Working very hard for something

- Implies exerting a lot of effort towards a goal, but doesn't capture the futility aspect of a "wild goose chase."

- Option 3: To betray someone

- This means to be disloyal or treacherous, which is not related to the idiom in question.

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