In this paper, a new attack model in which the number of colluders are distributed according to a certain probability distribution is introduced. Two classes of collusion attacks which include well-known collusion attacks in the context of multimedia fingerprinting are provided. For these two attack classes, achievable rates for the unknown size of the actual colluders are derived. Based on the derived achievable rates, achieve rates for some particular attacks are investigated. For the AND attack, the bound derived in this paper coincides with the previous known bound, although the attack model in this paper does not assume that the decoder knows the actual number of colluders. Moreover, for the averaging attack, it is clarified that derived achievable rate is larger than previously known bound with random linear codes.