Let [Formula: see text] be a simplicial complex. In this paper, we study random sub-hypergraphs and sub-complexes of text]. By considering the minimal complex that sub-hypergraph can embedded in maximal sub-hypergraph, define some maps on space probability functions We compositions these as well their actions functions.

 Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+...