Source : Webster's Revised Unabridged Dictionary (1913)

Hopeful \Hope"ful\, a.
   1. Full of hope, or agreeable expectation; inclined to hope;
      expectant.

            Men of their own natural inclination hopeful and
            strongly conceited.                   --Hooker.

   2. Having qualities which excite hope; affording promise of
      good or of success; as, a hopeful youth; a hopeful
      prospect. ``Hopeful scholars.'' --Addison. --
      {Hope"ful*ly}, adv. -- {Hope"ful*ness}, n.

Source : WordNet®

hopefully
     adv 1: with hope; in a hopeful manner; "we searched hopefully for a
            good position" [ant: {hopelessly}]
     2: it is hoped; "hopefully the weather will be fine on Sunday"