  We describe the method used by the Multi-Band Template Analysis (MBTA)
pipeline to compute the probability of astrophysical origin, $p_{astro}$, of
compact binary coalescence candidates in LIGO-Virgo data from the third
observing run (O3). The calculation is performed as part of the offline
analysis and is used to characterize candidate events, along with their source
classification. The technical details and the implementation are described, as
well as the results from the first half of the third observing run (O3a)
published in GWTC-2.1. The performance of the method is assessed on injections
of simulated gravitational-wave signals in O3a data using a parameterization of
$p_{astro}$ as a function of the MBTA combined ranking statistic. Possible
sources of statistical and systematic uncertainties are discussed, and their
effect on $p_{astro}$ quantified.
