  We compute the first cohomology of the ortosymplectic Lie superalgebra
$\mathfrak{osp}(1|2)$ on the (1,1)-dimensional real superspace with
coefficients in the superspace $\frak{D}_{\lambda,\nu;\mu}$ of bilinear
differential operators acting on weighted densities. This work is the simplest
superization of a result by Bouarroudj [Cohomology of the vector fields Lie
algebras on $\mathbb{R}\mathbb{P}^1$ acting on bilinear differential operators,
International Journal of Geometric Methods in Modern Physics
  (2005), {\bf 2}; N 1, 23-40].
