While it depends on the airline/airport, there are three different types of screening going on. Only one of the three is "random screening".
One is the profiling by the CAPS software the airlines are all using. It will indicate on the screen or boarding pass that the person needs additional screening based on some factor that fit the profile, or they may print out a list to use at the gate. They were not randomly selected, they were profiled.
Second is the continuious screening. That is where somebody has to be screened all the time the plane is boarding, until everybody is onboard. By definition, the first person in line then has to be screened. If he's not then they are not continuiously screening people. It's not random, it's the first person in line, when they are done with them, they take the next person coming by, unless one of the profiled people gets put in queue. Why anybody would be first in line when this has been going on for so many months is beyond comprehension.
The last is random, where the same profiling software picks some set number of people at random for additional screening. If they told you how it was being done, then it wouldn't be random.
So while the first person is almost guaranteed to be selected, it's not a random selection, they were chosen because they were first in line. When they are done, the next person will be selected, that too isn't random, it was because they were next in line. It'd not random the guy who paid cash and is on the watch list was picked for screening, they were profiled.