For a gas turbine engine, a press release by GE gives some data as a reference point. In 1995 they quoted various engines as having a dispatch rate of between 99.99% and 99.89%. That is only 0.01 to 0.11 % of flights could not depart due to an engine issue. However, that doesn't identify in flight failures, best captured by the inflight shut down (IFSD) rate. Data on this is difficult to get for specific engines, as the OEMs consider it competitive information, so the best guide is probably as mentioned the ETOPS rating. The ETOPs fleet is reported as achieving a shut down rate of less than 0.01 per 1000 engine hours.
Also, Stats on the actual engine (pulled from a 1997 GE Report), as well as a stackexchange answer. Neither which include stats of actual uncontained engine failures. sauces for consideration:
https:// aviation.stackexchange.com/questions/42627/how-common-is-engine-failure
https:// www.geaviation.com/press-release/cf6-engine-family/ge-aircraft-engines-commercial-engine-status-report-0