  We report a study of the CUORE sensitivity to neutrinoless double beta
($0\nu\beta\beta$) decay. We used a Bayesian analysis based on a toy Monte
Carlo (MC) approach to extract the exclusion sensitivity to the
$0\nu\beta\beta$ decay half-life ($T_{1/2}^{0\nu}$) at $90\%$ credibility
interval (CI) -- i.e. the interval containing the true value of
$T_{1/2}^{0\nu}$ with $90\%$ probability -- and the $3 \sigma$ discovery
sensitivity. We consider various background levels and energy resolutions, and
describe the influence of the data division in subsets with different
background levels. If the background level and the energy resolution meet the
expectation, CUORE will reach a $90\%$ CI exclusion sensitivity of
$2\cdot10^{25}$ yr with $3$ months, and $9\cdot10^{25}$ yr with $5$ years of
live time. Under the same conditions, the discovery sensitivity after $3$
months and $5$ years will be $7\cdot10^{24}$ yr and $4\cdot10^{25}$ yr,
respectively.
