The security department at New York airport is observing the arrivals of people, each arriving person may or may not be Pakistani. An arriving person will be Pakistani with probability p, independent of any other arriving person. They observe the people until they see two Pakistanis. Let X equal the number of people up to and including the 1st Pakistani. Let Y equal the number of people up to and including the 2nd Pakistani. Find the conditional PMFs PX|Y(x|y) and PY|X(y|x).