A large corporation receives express mail deliveries at its main office in New York daily. The express mail is delivered by two firms: Fad Express and Emerald. From recent corporate data, 60 percent of the deliveries are made by Fad Express and 40 percent by Emerald. Both
companies guarantee delivery by 11 a.m. Also, based on recent data given that Fad Express made the delivery, the probability it was late (i.e. arrived after 11 a.m.) is 0.10 and if Emerald made the delivery, the probability that it was late is 0.20. An express mail delivery arrived late in the main office in New York. What is the posterior probability that it was delivered by Emerald?