Mutation recurrence is then modeled using the Poisson binomial distribution, which accounts for variation in mutation rate across tumors. For a specific region of interest, the probability of having mutations in k or more individuals is given by:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pr \left( {K \ge k} \right) = \mathop {\sum }\limits_{m = k}^n \mathop {\sum }\limits_{A \in F_m} \mathop {\prod }\limits_{i \in A} p_i\mathop {\prod }\limits_{j \in A^c} (1 - p_j)$$\end{document}PrK≥k= ∑m=kn ∑A∈Fm ∏i∈Api ∏j∈Ac(1-pj)