When noise is present, the outcome of the competition between two species is no longer a deterministic function of the initial population sizes. An approximate value is given for the probability that a specified species will become extinct, conditioned on the initial population sizes. The calculation involves the asymptotic solution of the Kolmogorov backward equation. The theory is compared with Monte Carlo experiments for the case of flour beetle competition. It is also shown that the theory can be used to describe threshold fluctuations in nerves.