In population genetics, the probability that an allele will become the only allele present in the population at some future point in time (it is not typically a permanent state). The fixation probability is some function of population size, intensity of selection on the allele, and the current frequency of the allele in the population.
The fixation probability of a beneficial allele with selection coefficient s is approximately 2s. Thus, an allele that conveys a 10% fitness advantage has only a 0.2 probability of fixing.