# [Pylongolf2][1], 11 bytes

    1r1=?1>~<¿
Explanations:

    1           push 1 to the stack
     r          pick a random number between 0 and 1
      0=        push 1 to the stack and compare them
        ?1>~<¿  if true, push 1 to the stack then print it forever.
                terminate


  [1]: https://github.com/lvivtotoro/pylongolf2/