We report a study of the CUORE sensitivity to neutrinoless double beta (0νββ) decay. We used a Bayesian analysis based on a toy Monte Carlo (MC) approach to extract the exclusion sensitivity to the 0νββ decay half-life (T^0ν_1/2) at 90% credibility interval (CI) — i.e. the interval containing the true value of T^0ν_1/2 with 90% probability — and the 3σ 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 × 10²⁵ yr with 3 months, and 9 × 10²⁵ yr with 5 years of live time. Under the same conditions, the discovery sensitivity after 3 months and 5 years will be 7 × 10²⁴  and 4 × 10²⁵ yr, respectively.