If matter and antimatter were produced equally during the big bang, where is the rest of the antimatter? As far as my understanding goes, during the 'Big Bang' equal amounts of matter and antimatter (matter's oppositely charged twin) were produced, and the physical matter that remains within this universe is what's left over from the equilibrium of matter and antimatter canceling one another out following the Big Bang. If matter and antimatter truly do cancel one another out (are transformed into pure energy) upon contact, than:
a) why is there still matter in existence?
b) if matter is still in existence then doesn't that mean that somewhere within the universe there is an equal amount of antimatter?
 A: The link Kyle gives in  his comment expands enough on the reasons
a) why is there still matter in existence?.
That there exists matter as we know it is an experimental observation that has to be taken into account in any theoretical formulation. 
The existence of matter and antimatter is an experimental observation in the elementary particles data in our labs. The theories developed to describe the data are dominated by the CPT theorem :

CPT symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P and T that's observed to be an exact symmetry of nature at the fundamental level. The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry

Within this theory CP transformations turn particles into antiparticles.  There exist CP violation processes in the data,   but the size is not enough to explain the predominance of matter in our observable universe. Other arguments are brought forth as in the link above.
The CP violation  subject is still a matter of research, experimentally and theoretically.

b) if matter is still in existence then doesn't that mean that somewhere within the universe there is an equal amount of antimatter?

All the observational data from astrophysics lead to the conclusion that in the observable universe matter dominates by orders of magnitude.
1) a probe was just landed on a comet , no  explosion
2) cosmic rays from sun and the galaxy are predominantly matter
3)there is no dominant signal in cosmic gamma rays of electron positron annihilation that would happen in the boundary of galaxies and clusters of galaxies if they were composed of different matter content.
So it is an observational fact that the observable universe is dominated by matter, and the explanation is a matter of research still.
