Plasmids with the 2 μ plasmid origin are commonly-used in the genetic engineering of the budding yeast Saccharomyces cerevisiae. Intracellular copy numbers of 2 μ plasmids are different depending on the genes inserted into the plasmids. This difference is thought to occur from the difference in the growth efficiency （fitness） produced by the positive- and negative-selection biases of genes inserted in the plasmid. In this study, we made a mathematical model based on this assumption. Computational simulations of the model validated that copy numbers of the plasmids are rapidly settled depending on the fitness created by the gene on the plasmid. The copy number of a plasmid only contains a bias to keep the plasmid in a single copy became average 20copies per cell when the plasmid is randomly distributed, suggesting that no positive distribution mechanism is required for a plasmid to become multicopy.