Transmission system outages (mostly caused by exogenous events) are among the major causes of large blackouts, and thus models to determine the uncertainty of transmission outages in large power network planning problems are becoming critical. In this context, this paper proposes a mixed-integer linear programming (MILP) approach to solve the transmission investment planning problem considering n - k security criterion. The objective is to minimize the investment and the expected operational costs subject to a comprehensive set of operational constraints under any contingency state comprising the simultaneous loss of up to k transmission lines. Due to the exponentially large number of possible contingency states, a sample average approximation (SAA) method is applied to make the optimization problem computationally tractable. Our proposed approach is implemented on the IEEE 24-bus and IEEE 118-bus test systems. This approach provides an optimization framework to comprise and analyze the impact of the sample size on the variability of the estimated results.