  We investigate the first-passage properties of nearest-neighbor hopping on a
finite interval with disordered hopping rates. We develop an approach that
relies on the backward equation, in conjunction with probability generating
functions, to obtain all moments, as well as the distribution of first-passage
times. Our approach is simpler than previous approaches that are based on
either the forward equation or recursive method, in which the $m^{\rm th}$
moment requires all preceding moments. For the interval with two absorbing
boundaries, we elucidate the disparity in the first-passage times between
different realizations of the hopping rates and also unexpectedly find that the
distribution of first-passage times can be \emph{bimodal} for certain
realizations of the hopping rates.
