Suppose that tracing a ray in your scene takes time A on average, while evaluating the BRDF on a pair of vectors takes time B.
(a) In tracing N rays from the eye using path tracing, using a fixed attenuation rate r (so that a path is extended at each point with probability (1 - r)), estimate the time taken in terms of A and B (assume all other operations are free).
(b) Consider tracing N/2 rays from the eye and N/2 rays from the single light source in a scene using bidirectional path tracing; do the same computation.