Probabilistic realizations of outages and their effects on the operational costs are highly overlooked aspects in power system expansion planning. Since the effect of randomness in contingencies can be more prominent especially when transmission switching is considered, in this paper we introduce contingency-dependent transmission switching concept to ensure N-1 criterion. To include randomness of outages and the outputs (i.e. flow on the lines/generation amounts) during the outages, we represent each contingency by a single scenario. Status of transmission lines, generation amounts and power flow decisions are defined as recourse actions of our two-stage stochastic model, therefore, expected operational cost during the contingencies are taken into account in a more accurate manner. A solution methodology with a filtering technique is also proposed to overcome the computational burden. The model and the solution methodology are tested on the IEEE Reliability Test System and IEEE 118-bus power system and the results show that the solution method finds the solutions for these power systems in significantly shorter solution times. The solution method is also tested on a new data set for the 380-kV Turkish transmission network. Suggestions for possible extensions of the problem and the modifications of the solution approach to handle these extensions are also discussed.