Given a set of urns, each filled with a mix of black chips and white chips, what is the probability of drawing a black chip from the last urn after some sequential random shifts of chips among the urns? The Total Probability Formula (TPF) is the common tool to solve such a problem. However, when the number of urns is more than two and the number of shifted chips is not small, using the TPF becomes impractical or even impossible. This note presents a much simpler alternative formula to the TPF in dealing with the probability problem. As a byproduct, a recursive formula for computing the probabilities of sequential events is derived and a closed form of the recursive solution is also presented. These results could potentially be applied to estimating the demographic distribution of students after a chain of transfers as well as the biological studies of mutation.