Engineers at Rocketdyne, the manufacturer, estimate the total probability [of catastrophic failure] as 1/10,000. Engineers at Marshal estimate it as 1/300, while NASA management, to whom these engineers report, claims it is 1/100,000. An independent engineer consulting for NASA thought 1 or 2 per 100 a reasonable estimate.
— Personal observations on the reliability of the Shuttle (Rogers Commission Appendix F) by R.P. Feynman
Actual statistics from the life of the shuttle, last flown as STS-135 8 - 21 July, 2011:
Presumably, those estimates are just for the Space Shuttle Main Engines (SSME/RS-25), give that's what Rocketdyne was manufacturing and propulsion is one of Marshall Spaceflight Center's fortes.
— Personal observations on the reliability of the Shuttle (Rogers Commission Appendix F) by R.P. Feynman
Actual statistics from the life of the shuttle, last flown as STS-135 8 - 21 July, 2011:
Total launches 135
Failures 2
Successes 133
Failure rate: 1.5%