From hare +‎ brained.

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harebrained (comparative more harebrained, superlative most harebrained)

(of an idea or plan etc) Absurd, foolish or stupid.
Synonyms: see Thesaurus:stupid
- 2008, Sarah McCarty, Promises Reveal, Penguin, →ISBN:
  “Now why do I get the feeling we're not talking about the harebrained plan you came up with?” “It wasn't harebrained.” “Did it have you going within twenty feet of a whorehouse at night, unchaperoned?” He knew darn well it did.
(of a person) Frivolous and silly; featherbrained or scatterbrained; stupid.
Synonyms: absent-minded, half-brained; see also Thesaurus:stupid
- 1722, Daniel Defoe, Moll Flanders, The Author's Preface:
  Her getting a parcel from a hare-brained wench at the coaches in St. John Street; her booty made at the fire, and again at Harwich, all give us excelle

featherbrained or scatterbrained

English