1 IntroductionIn 1961, Erd˝os, Ko and Rado proved that if 2r 6 n, then the edge set E of anintersecting r-uniform hypergraph with vertex set V and | V | = n cannot have larger sizethan, moreover if 2r the form { e ∈: v ∈ e} for some fixed v ∈ V . In the past almost five decades, thearea of intersection theorems has been widely studied, but randomized versions of theErd˝os-Ko-Rado theorem have only attracted the attention of researchers recently. Thereare mainly two approaches to the randomized problem. Balogh, Bohman and Mubayi considered the problem of finding the largest intersecting hypergraph in the probabilityspace G(n, p) of all labeled r-uniform hypergraphs on n vertices where every hyperedgeappears randomly and independently with probability p = p(n). In this paper, we followthe approach of Bohman et al. , . They considered the following process to generatean intersecting hypergraph by selecting edges sequentially and randomly...