Primary fragmentation of coal plays an important role in overall combustion efficiency. In practice, a mixture of different sized coal particles is used. Numerical simulation of primary fragmentation of coal particle mixture subjected to shock wave is studied in this work. Coal particles behind shock wave undergo heating, volatilization, and fragmentation. Each of these is modeled in the simulation. Heat transfer is linked with volatilization and solid mechanics to predict primary fragmentation of coal particles using a probabilistic and statistical approach. Fracture time and fracture location are identified by setting fracture criteria, which is obtained using failure probability calculated from Weibull's Weak Link theory. Irregularities inside a coal particle are included through Weibull's parameters. Average fracture time of mixture of coal particles is calculated. Numerical results suggest that approximately 90% of coal particles in the mixture have fractured in about 1-2 ms. Simulation results suggest that in the timescale of interest thermal stress dominated, with only marginal effects due to volatilization.