R, 30 22 bytes
###code cat(runif(1)<1/scan()) #new f=function(N)cat(runif(1)<1/N) #old
code
cat(runif(1)<1/scan()) #new
f=function(N)cat(runif(1)<1/N) #old
It generates a number from a uniform distribution (0 to 1) and should evaluate to true 1/n of the times.