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The merger and accretion probabilities of dark matter halos have so far onlybeen calculated for an infinitesimal time interval. This means that aMonte-Carlo simulation with very small time steps is necessary to find themerger history of a parent halo. In this paper we use the random walk formalismto find the merger and accretion probabilities of halos for a finite timeinterval. Specifically, we find the number density of halos at an earlyredshift that will become part of a halo with a specified final mass at a laterredshift, given that they underwent $n$ major mergers, $n=0,1,2,...$ . Wereduce the problem into an integral equation which we then solve numerically.To ensure the consistency of our formalism we compare the results withMonte-Carlo simulations and find very good agreement. Though we have done ourcalculation assuming a flat barrier, the more general case can easily behandled using our method. This derivation of finite time merger and accretionprobabilities can be used to make more efficient merger trees or implementeddirectly into analytical models of structure formation and evolution.

Dark matter halo merger and accretion probabilities in the excursion set formalism