Quantifying the statistical error in a counting experiment

[JoePhysicsNut]

I need to find the statistical error in a counting experiment. Specifically, a decay can proceed via option A or option B and I need to find the branching ratio BR_a=(N_a)/(N_a+N_b). If I were to do this counting experiment multiple times my results for BR_a would follow the binomial distribution since there are two decay channels.

How do I quantify the statistical error in my result given that I conduct the experiment only once?

 

[mfb]

Do you have a fixed number of decays ("I take data until I have 100 decays in those two channels")?
No => you can treat N_a and N_b as the result of independent Poisson processes.
Yes => the denominator is fixed, and N_a comes from a binomial distribution.

 

[Meir Achuz]

The usual statistical error gives N_A+ - sqrt{N_A}.