  We propose an extension of the asynchronous pi-calculus with a notion of
random choice. We define an operational semantics which distinguishes between
probabilistic choice, made internally by the process, and nondeterministic
choice, made externally by an adversary scheduler. This distinction will allow
us to reason about the probabilistic correctness of algorithms under certain
schedulers. We show that in this language we can solve the electoral problem,
which was proved not possible in the asynchronous $\pi$-calculus. Finally, we
show an implementation of the probabilistic asynchronous pi-calculus in a
Java-like language.
