Trigger[n_, N_, dt_, f_] := P[n, N, dt, f]*P[0, N, 5/10^9, f]*
     P[1, N, 5/10^9, f]*(10^9/5)
 
P[n_, N_, dt_, f_] := PDF[BinomialDistribution[N, p[dt, f]], n]
 
PDF /: PDF::usage = "PDF[distribution, x] gives the probability density \
function of the specified statistical distribution evaluated at x."
 
p[dt_, f_] := 1 - Exp[(-dt)*f]