Final answer:
The outcome when two indistinguishable photons hit a beam splitter, due to the Hong-Ou-Mandel effect, is that they will either both be transmitted or both reflected. Absorption is not considered for an ideal beam splitter.
Step-by-step explanation:
When two indistinguishable photons hit a beam splitter, quantum mechanics tells us that each photon has a probability of being either transmitted or reflected. However, due to a quantum phenomenon known as quantum interference, the two photons will either both be transmitted or both be reflected assuming they are identical in all properties and synchronized. This is because of the way their wave functions combine at the beam splitter; the outcomes where one photon is transmitted and one is reflected interfere destructively, and therefore are not observed. This phenomenon is part of what's known in quantum mechanics as the Hong-Ou-Mandel effect. Note that the photons being absorbed is not typically considered in this idealized situation, and a perfect beam splitter does not absorb photons; it only transmits or reflects them.
The answer to the question about the outcome when two indistinguishable photons hit a beam splitter is that the photons will either both be transmitted (a) or both be reflected (b).