Scattering MC toy model

I would like to make a scattering toy simulation as a computational physics project. I’m having issues visualizing which parameter of the scattering function I need to compare with the randomly generated number to consider that the event was scattered or not.

Using
$$
frac{dsigma}{dOmega} = frac{1}{rho_n t Delta Omega} frac{mathrm{Flux_{scattered}}}{mathrm{Flux_{incident}}}
$$
where $rho_n$ is the nuclear density of the material that will scatter, $t$ is the thickness, and $Delta Omega$ = $4pi$ since in this toy model the detector will be a sphere around the scattering (and then I won’t need to integrate). If I know the total cross-section $sigma_{tot}$, is it ok to do something like this:

• Generate $N$ random numbers $n_i$

• If $n_i le 4pi sigma_{tot} $ then I had a particle scattered