In this paper we introduce formulae for estimating the failure rate of a large scaled software by using the Bayesian rule when a black-box random testing which selects an element(test case) at random with equally likely probability, is performed. A program or software can be treated as a mathematical function with a well-defined (input)domain and range. For a large scaled software, their input domains can be partitioned into multiple subdomains and exhaustive testing is not generally practical. Testing is proceeding with selecting a subdomain, and then picking a test case from within the selected subdomain. Whether or not the proportion of selecting one of the subdomains is assumed probability, we developed the formulae either case by using Bayesian rule with gamma distribution as a prior distribution.