One of the key components of bin microphysics schemes is the quasi‐stochastic collection equation that describes the collection process of cloud particles. The normal quasi‐stochastic model, hereafter the NQS model, assumes that the time step is infinitesimally small, so that a cloud particle can collide with other cloud particle only once within the time step. However, since the time step is finite, a cloud particle can collide with other cloud particle more than one time within the time step. Hence, the improved quasi‐stochastic model that realizes this approach, hereafter the IQS model, is physically more reasonable. This study provides the evaluation of the IQS model against the NQS model in precipitation prediction. For this, a precipitation event observed over north central Mongolia on 21 August 2014 is simulated using the Weather Research and Forecasting model with a detailed bin microphysics scheme. The surface precipitation amount is larger in the IQS model than in the NQS model, particularly over the strong precipitation region. The IQS model increases the mass contents of small drops and large drops due to multiple collisions. The increased large drops contribute to the increase in surface precipitation amount. The increased small drops are transported upward, which eventually leads to an increase in snow mass content. Deposition and riming in the IQS model occur more actively, further increasing snow mass content. The increased snow mass content also contributes to the increase in surface precipitation amount through melting.