After the big bang occurred what biased the formation of particles over anti-particles? Why are particles more common than anti-particles?
Currently, there's no single explanation for this.
The simplest explanation is that there isn't any imbalance — there are large antimatter bodies in the universe; just separated from us. However, these would have to be pretty far away (otherwise the boundary annihilation would be detectable). Theoretically, this requires antimatter to have clumped early on, which is rather unlikely/impossible.
A far more likely explanation is that charge-parity symmetry is violated. In other words, flipping the charges and parities in a reaction may not lead to the same dynamics — the outcome (when the charge/parity is flipped back) or distributions of outcomes may not be the same. Usually, we expect that if we flip the charges on both sides of a reaction, the reaction proceeds in the same manner (with same probabilities, etc). There is evidence that suggests that this may not be true. If this is indeed the case, then the matter-antimatter imbalance is not that hard to explain.