A population balance model is developed for the prediction of the average gas holdup and axial gas holdup profile in the bubble columns operating in the homogeneous regime. The model takes into account the effect of bubble expansion along the column height and thus it is applicable to tall columns such as flotation columns in the mineral processing industries. The model captures the effect of superficial gas and liquid velocities, bubble rise velocity, operating pressure, and column height on the gas holdup. In the case of flotation columns, because of the presence of surfactants in the liquid phase, froth is observed at the top of the column. Typically, froth shows the axial profile of gas holdup and the mean bubble size, indicating that the coalescence is an important phenomenon to describe the dynamics of the froth. A probabilistic perspective is developed to address the bubble coalescence process occurring in the froth and the bubble transition probability for coalescence is obtained from experimental data in the literature.