A market research company has approached you about the possibility of using its services to help you decide whether to launch a new product. According to its customer portfolio, it has correctly predicted a favorable market for its clients' products 14 out of the last 16 times. It has also correctly predicted an unfavorable market for its clients' products 9 out of 11 times. Without this research company's help, you have estimated the probability of a favorable market at 0.55. Calculate the posterior probabilities, using the track record of the research firm.