If the Wikipedia page on Boltzmann brain is accurate, then the probability is surprisingly (but relatively) high.
> The Boltzmann brain gained new relevance around 2002, when some cosmologists started to become concerned that, in many theories about the universe, human brains are vastly more likely to arise from random fluctuations; this leads to the conclusion that, statistically, humans are likely to be wrong about their memories of the past and in fact be Boltzmann brains. When applied to more recent theories about the multiverse, Boltzmann brain arguments are part of the unsolved measure problem of cosmology.
> The Boltzmann brain gained new relevance around 2002, when some cosmologists started to become concerned that, in many theories about the universe, human brains are vastly more likely to arise from random fluctuations; this leads to the conclusion that, statistically, humans are likely to be wrong about their memories of the past and in fact be Boltzmann brains. When applied to more recent theories about the multiverse, Boltzmann brain arguments are part of the unsolved measure problem of cosmology.