There Are Three General Locations That a Taxi Can Go

There are three general locations that a taxi can go to: the airport, downtown, and elsewhere. When a taxi driver starts in the downtown location, there is a 0.40 chance that his first call will take him to the airport and a 0.40 chance of going to another downtown location. Once a taxi is at the airport, there is a 0.80 probability that the next fare will take him downtown and a 0.20 chance of going elsewhere. The probability of a call from anywhere except downtown taking him to the airport is 0.20. Therefore, the probability that the taxi is at the airport when the third call arrives after going on shift is 0.20.