Central Au - Au collision.
L - Beam Luminosity. 
At RHIC, beam is made of
n = 60 bunches of Golden nuclei,
k = 109 particles in a bunch.
f is a frequency of bunches passing some particular point (Beam-Beam Counters). 
,
c - speed of light,
C=3.84km - RHIC' circumference, so 
T - time spacing between bunches, 
Finally, RHIC claims: 
- Collision Crossection.
Let's consider collisions with impact parameter of RAu, then 
;
where 
. So, 
Final result is, that we expect to have about 570 Collision Events per second. Because of the symmetry, that means 570 coincidence events in both arrays per second.
Beam - Gas (He4) collisions.
Rblue=Ryellow - Individual Beam-Gas Collision Rate; 
F - Flux of Particles (Number of particles per second), 
, where 
, so 
Nbp - Number of He4 particles inside the beam-pipe per cm3.
Obviously, that 
, where Patm is atmospheric pressure.
, and 
. So, 
l - Length of the Interaction Region; 
Finally, 
Final result is, that we expect to have approximately .04 Random Coincidence events per second. Our numbers basically agree with the other experiments. Here is a PDF file to compare.
GEANT Simulations and Final Conclusion.
We tried to answer the same question with the help of a GEANT simulations. 4 files were generated: AuAu MinBias, AuO in the right and left directions of the Au beam and AuAu Central Collisions. Here is the picture of hits vs. number of tubes hit. By look at this picture and taking into consideration all above calculations one can make a conclusion, that restriction of 2 hit coincidences would work perfectly as a trigger, cutting out most part of the beam-gas collisions and leaving us most of the good beam-beam collisions events.
