Why does Hawking Radiation not add up to zero?

Question

First off: I am not familiar with the details of quantum mechanics or relativity. My understanding of Hawking radiation is as follows: Pairs of particles and anti-particles can and will spontaneously form in space and when that happens near the event horizon of a black hole the anti-particle might fall into the black hole and the particle not, effectively causing the black hole to lose mass.

Now, this is totally fine with me. The thing I do not understand is: Why do more anti-particles fall into the black hole than particles? If these pairs pop up randomly, shouldn't the effects of Hawking-radiation and anti-Hawking-radiation cancel out?

Answer 1

What do you mean, "cancel out"? Even if a particle and its antiparticle annihilate, energy is still conserved, e.g. an electron annihilating with a positron gives two photons (well, depending on their energy). The radiated energy can't just vanish without a trace.