  The latest binary black hole population estimates argue for a subpopulation
of unequal component mass binaries with spins that are likely small but
isotropically distributed. This implies a non-zero probability of detecting
spin-induced orbital precession and higher order multipoles moments in the
observed gravitational-wave signals. In this work we directly calculate the
probability for precession and higher order multipoles in each significant
gravitational-wave candidate observed by the LIGO--Virgo--KAGRA collaborations
(LVK). We find that only one event shows substantial evidence for precession:
GW200129_065458, and two events show substantial evidence for higher order
multipoles: GW190412 and GW190814; any evidence for precession and higher order
multipoles in other gravitational-wave signals is consistent with random
fluctuations caused by noise. We then compare our observations with
expectations from population models, and confirm that current population
estimates from the LVK accurately predict the number of observed events with
significant evidence for precession and higher order multipole moments. In
particular, we find that this population model predicts that a binary with
significant evidence for precession will occur once in every $\sim 50$
detections, and a binary with significant evidence for higher order multipole
moments will occur once in every $\sim 70$ observations. However, we emphasise
that since substantial evidence for precession and higher order multipole
moments have only been observed in three events, any population model that
includes a subpopulation of binaries yielding $\sim 2\%$ of events with
detectable precession and higher order multipole moments will likely be
consistent with the data.
