A natural probabilistic model for motif discovery has been used to experimentally test the quality of motif discovery programs. In this model, there are $k$ background sequences, and each character in a background sequence is a random character from an alphabet $\Sigma$. A motif $G=g_1g_2...g_m$ is a string of $m$ characters. Each background sequence is implanted a probabilistically generated approximate copy of $G$. For a probabilistically generated approximate copy $b_1b_2...b_m$ of $G$, every character $b_i$ is probabilistically generated such that the probability for $b_i\neq g_i$ is at most $\alpha$. We develop three algorithms that under the probabilistic model can find the implanted motif with high probability via a tradeoff between computational time and the probability of mutation. The methods developed in this paper have been used in the software implementation. We observed some encouraging results that show improved performance for motif detection compared with other softwares.