The size of the radius of the event horizon of a black hole created by the merger of a black hole binary system Let's assume that you had a black hole binary system and everything said here is possible. Their large masses would lead to a large emission of gravitational waves. The loss of orbital energy and angular momentum to this gravitational radiation should ultimately cause the two black holes to merge into a single black hole containing the combined mass of the merged black holes.

With this said, does a greater combined mass of the newly formed black hole mean that the radius of the new event horizon is greater than the radius of the event horizons of the singular black holes? 
I don't know if there is a formula connecting mass to radius, or if this is essentially a conceptually hypothetical concept, and the answer is simply that the larger the mass of the black hole, the larger the radius of its event horizon
The "radius" (there is no physical surface) of the event horizon of a rotating black hole, depends on both it's mass $M$ and angular momentum $J$, and is given by the equation
$$ r = \frac{GM}{c^2} +\sqrt{\left(\frac{GM}{c^2}\right)^2- \left(\frac{J}{Mc}\right)^2}.$$ 

It is thus difficult (for me anyway) to give a straightforward answer to your question. When two black holes merge, they will each have their own masses and angular momenta, plus there will be angular momentum in the orbit. The gravitational waves emitted during the merger can take away mass from the system as a whole (e.g. the final mass of the first observed black hole merger was three solar masses less than the summed masses of the merging components).

So, in general yes, for non-spinning black holes the event horizon grows as the total mass. But if the merger results in a black hole with maximal spin, where $J = GM^2/c$, then the final event horizon could be half the size given by the Schwarzschild radius ($2GM/c^2$), even though the total mass is larger than the black holes that contributed to it.

However, I think what is certainly true, is that it is not possible to add mass (even in the form of another black hole) to a given black hole and for the event horizon to get smaller, whatever the angular momentum contributed by that mass (section 4.2 of "Black Holes", by Raine &amp; Thomas, 2015, Imperial College Press).