California Consulting, LLC is a consulting business operated by Dr. Matecki and one of his colleagues. In a typical year, California Consulting responds to 12 requests for proposals (RFPs) in hopes of obtaining business. Each RFP results in either a 'success' (California Consulting is awarded the contract) or a 'failure' (California Consulting does not win the business). Assume that the outcomes follow the binomial distribution with the probability of success equal to 0.4.

One particular RFP has been submitted for a large research project. I initially felt that there was a 50-50 chance of getting the project; however, the agency to which the bid was submitted as subsequently asked for additional information on the bid. Past experience indicates that on 80% of the successful bids and 35% of the unsuccessful bid, the agency requested additional information.

a. Compute the posterior probability that the bid will be successful given that a request for additional information has been received.