  Gravitational wave observations of the ringdown of the remnant black hole in
a binary black hole coalescence provide a unique opportunity of confronting the
black hole no-hair theorem in general relativity with observational data. The
most robust tests are possible if multiple ringdown modes can be observed. In
this paper, using state-of-the-art Bayesian inference methods and the most
up-to-date knowledge of binary black hole population parameters and ringdown
mode amplitudes, we evaluate the prospects for black hole spectroscopy with
current and future ground based gravitational wave detectors over the next 10
years. For different population models, we estimate the likely number of events
for which the subdominant mode can be detected and distinguished from the
dominant mode. We show that black hole spectroscopy could significantly test
general relativity for events seen by the proposed LIGO Voyager detectors.
