<>, 27 + 3 for -v = 30 bytes =============
Here is a not-uniform-at-all solution where I mod N the sum of 15876 random picks of 0 or 1 :
0"~":*>:?vr%0=n;
1-$1+$^-1x
N must be input on the stack with -v flag, output is 0 for falsey and 1 for truthy.
A much smarter and uniform solution that work for 1/2^N instead :
4{:?!v1-}:">"$2p:"x"$3p:"^"$4p1+:">"$3p1+!
^1<
0n;
1n;>
For an input 3 you've got 1/8 chances of getting 1 and 7/8 of getting 0.
Explanation :
I append as much x as needed on the 4th line and surround them with directions so there is only two ways out of the x: either the falsey output or the next x. If all x go in the right direction, the last one will route to the truthy output.
For example for N=5, the final codespace is the following :
4{:?!v1-}:">"$2p:"x"$3p:"^"$4p1+:">"$3p1+!
^1<
0n; > > > > >
1n;>x>x>x>x>x>
^ ^ ^ ^ ^