Statistics for Measurement of the ratio of the production cross sections times branching fractions of $B_{c}^{\pm} \to J/\psi \pi^{\pm}$ and $B^{\pm} \to J/\psi K^{\pm}$ and $\mathcal{B}(B_{c}^{\pm} \to J/\psi \pi^{\pm}\pi^{\pm}\pi^{\mp})/\mathcal{B}(B_{c}^{\pm} \to J/\psi \pi^{\pm})$ in pp collisions at $\sqrt{s} =$ 7 TeV