The probability of fixation of a mutant gene in a population depends on both selection and random genetic drift. Kimura extended previous results to include any level of dominance, deriving a general formula for the probability of eventual fixation, u(p), which accounts for random fluctuations in selection intensity and genetic drift. This formula is used to solve the question of "quasi-fixation" posed by the author in 1955. The derivation involves a continuous stochastic process, leading to a partial differential equation known as the Kolmogorov backward equation. The solution to this equation gives the probability of fixation, u(p), which depends on the initial frequency of the gene, p, and the mean and variance of the change in gene frequency per generation. The formula is shown to include previous results as special cases and is applied to problems involving random fluctuations in selection intensity. It is also used to show that even in large populations, an advantageous gene may be lost due to fluctuating selective values. The probability of fixation of an individual mutant gene in a randomly mating diploid population is given by u = u(1/(2N)), where N is the number of reproducing individuals. Applications include genic selection, zygotic selection, and random fluctuation of selection intensity. The results show that the probability of fixation depends on the selection coefficient, population size, and the variance of the selection intensity. The formula is also applied to completely recessive genes, showing that the probability of fixation is reduced when the gene is recessive. The results are compared with previous studies, showing agreement with the results of Fisher, Haldane, Wright, and Robertson. The paper concludes that the probability of fixation of a mutant gene in a population is influenced by both selection and random genetic drift, and that the formula derived provides a general solution to this problem.The probability of fixation of a mutant gene in a population depends on both selection and random genetic drift. Kimura extended previous results to include any level of dominance, deriving a general formula for the probability of eventual fixation, u(p), which accounts for random fluctuations in selection intensity and genetic drift. This formula is used to solve the question of "quasi-fixation" posed by the author in 1955. The derivation involves a continuous stochastic process, leading to a partial differential equation known as the Kolmogorov backward equation. The solution to this equation gives the probability of fixation, u(p), which depends on the initial frequency of the gene, p, and the mean and variance of the change in gene frequency per generation. The formula is shown to include previous results as special cases and is applied to problems involving random fluctuations in selection intensity. It is also used to show that even in large populations, an advantageous gene may be lost due to fluctuating selective values. The probability of fixation of an individual mutant gene in a randomly mating diploid population is given by u = u(1/(2N)), where N is the number of reproducing individuals. Applications include genic selection, zygotic selection, and random fluctuation of selection intensity. The results show that the probability of fixation depends on the selection coefficient, population size, and the variance of the selection intensity. The formula is also applied to completely recessive genes, showing that the probability of fixation is reduced when the gene is recessive. The results are compared with previous studies, showing agreement with the results of Fisher, Haldane, Wright, and Robertson. The paper concludes that the probability of fixation of a mutant gene in a population is influenced by both selection and random genetic drift, and that the formula derived provides a general solution to this problem.