  The Josephus problem is a well--studied elimination problem consisting in
determining the position of the survivor after repeated applications of a
deterministic rule removing one person at a time from a given group.
  A natural probabilistic variant of this process is introduced in this paper.
More precisely, in this variant, the survivor is determined after performing a
succession of Bernouilli trials with parameter $p$ designating each time the
person to remove. When the number of participants tends to infinity, the main
result characterises the limit distribution of the position of the survivor
with an increasing degree of precision as the parameter approaches the
unbiaised case $p=1/2$. Then, the convergence rate to the position of the
survivor is obtained in the form of a Central-Limit Theorem.
  A number of other variants of the suggested probabilistic elimination process
are also considered. They each admit a specific limit behavior which, in most
cases, is stated in the form of an open problem.
