The first passage time of random walks from one end to the other, of a segment of adisorderedlattice is considered. Disorder is modeled by prescribing random nearest neighbor jump probabilities to the lattice sites. We consider lattices with random barriers, random traps, and Sinai disorder. We present exact results on mean first passage time (MFPT) and disorder averaged MFPT. We investigate the nature of the distribution of MFPT over the disorder.