Abstract: This paper examines the likelihood of efficiency given stability in a competitive market (banking system). Apparently, a financial crisis emanates from instability and inefficiency in the financial system(s) wherein the banking system is a key institution. Therefore, our concern geared towards maintaining both stability and efficiency in the banking system to avoid global financial crisis (contagion effect) using Bayesian Techniques. We deciphered a 1-1 mapping between the stability & efficiency indexes. We also discovered variant forms of relationships existing between stability and efficiency indexes (scores). Our findings identified levels of Stability that are highly predictive of certain levels of efficiency. Sequel to these findings we recommend contingent planning; which makes plans considering possible actions, consequences, and objectives towards achieving the desired levels of stability and efficiency in the system.