When a photon hits the eye (the front) it has the choice of reflecting and refracting. That's your 50%. Actually it does both, as quantum theory dictates, but when it is observed, the state collapses to where it is either here or there. (see comic
Other facts:
Photons have no mass, and hence always travel at the speed of light in vacuum. When they appear to travel slower than the speed of light (eg in a medium), the photon is actually absorbed and re-emitted billions of times (requires quantum theory too to fully describe)
Mirrors are actually diffuse at the atomic level (there is no such thing as a flat surface at the atomic level, as there are no atoms with flat sides). The light actually emits in all directions at once (called a wavefront, akin to a wave created by dropping a stone in a pond), however all light that travels in one particular direction (the reflection angle) undergoes constructive interference, while light in all other directions experience destructive interference.
CDs, DVDs, etc. have grooves which are separated from each other only a few wavelengths in length, and this creates a strange effect. Photons that hit a groove get lost (for simplicity), and photons that hit the flat space between the grooves are emitted in all directions as a wavefront. The alternating present and absent wavefronts create a 'mirror' where multiple angles undergo constructive interference, and these angles depend on the wavelength too. Hence the rainbows.