Absorption probabilities for a random walk between two partiality absorbing boundaries: I

A biased random walk on a linear lattice bounded by one or two partially absorbing boundaries is considered. Al the boundaries, the particle is either lost from the system or turned back, and reduces to the classical problem of a random walk with absorbing and/or reflecting barriers. The probabilities of ultimate absorption at the boundaries are obtained, as well as the conditional mean for the number of steps before stopping given the absorption at a specified barrier The symmetries for the conditional mean are also given. Previous formulae are found to be in error.