The different roles played by multiplicative white and colored noise in a single-mode dye-laser model are investigated through the concept of first-passage-time (FPT) distributions. An analytic result for the skewness of the FPT distributions is presented and compared with experimental measurements and numerical simulations. The effects of multiplicative white and colored noise on the mean, variance, and coefficient of skewness are discussed. The simplified theoretical model can well describe the transient process of a dye laser.