  We propose an approximation for the probability of tipping when the speed of
parameter change and additive white noise interact to cause tipping. Our
approximation is valid for small to moderate drift speeds and helps to estimate
the probability of false positives and false negatives in early-warning
indicators in the case of rate- and noise-induced tipping. We illustrate our
approximation on a prototypical model for rate-induced tipping with additive
noise using Monte-Carlo simulations. The formula can be extended to close
encounters of rate-induced tipping and is otherwise applicable to other forms
of tipping.
  We also provide an asymptotic formula for the critical ramp speed of the
parameter in the absence of noise for a general class of systems undergoing
rate-induced tipping.
