We use a histogram Monte Carlo simulation method to calculate the scaling functions of the existence probability E(p) and the percolation probability P of the bond random percolation model on honeycomb lattices with aspect ratios of 0.5 and 2.0. We find that such different aspect ratios give quite different scaling functions near the critical region. However, they give a consistent critical point, critical exponents, and the thermodynamic order parameter from renormalization-group calculations. Some interesting theoretical problems related to this work are discussed.
