Looking around here on various sources (including related questions on this site), if my understanding is correct, when implementing a path tracer with a material which has both a diffuse term and a specular term, we can randomly choose whether to evaluate the diffuse or the specular ray then divide the result by the probability of choosing diffuse or specular.
For example if we have a material 50% specular, we would have:
If diffuse ray was chosen:
If specular ray was chosen:
Once diffuse/specular is chosen, we have to find which ray exactly we want to use for $incomingLight$. In my case I have a rough dieletric surface (not a perfect mirror) and I would like to use importance sampling and use for example a cosine weighted pdf for diffuse and a NDF weighted pdf for the specular term. I couldn't find a source for this particular case, but If my understanding is correct, I would end up with either:
if diffuse was chosen, or:
if specular was chosen. Is this result correct?