  We consider a randomised version of Kleene's realisability interpretation of
intuitionistic arithmetic in which computability is replaced with randomised
computability with positive probability. In particular, we show that (i) the
set of randomly realisable statements is closed under intuitionistic
first-order logic, but (ii) different from the set of realisable statements,
that (iii) "realisability with probability 1" is the same as realisability and
(iv) that the axioms of bounded Heyting's arithmetic are randomly realisable,
but some instances of the full induction scheme fail to be randomly realisable.
