Random selection is the opposite of thinking. It can be done in a couple of lines of programming in any modern language. You want 3% of all passengers to receive a random patdown? Generate a random number, x, between 1 and 100. If x is less than or equal to 3, blink the yellow light.

I've been through customs in Mexico, and everyone has to push a button. If you get a green light, you go through, a red light gets additional hand-searching. I've seen a thirty-year old man with a 70-lb suitcase patiently holding the hand of a 3-year old as her tiny backpack is searched. Totally random, and it may not make sense from a 'logical target' perspective, but if you wanted to sneak in something illegal, why not put it in the 3-year old's bag?

+1 - As long as there truly is a randomizer and not an excuse for a non-random selection by a TSO.

If 3% of passengers need to be hand-searched to generate uncertainty, (arguable, I know) I would rather have 3 randomly chosen, rather than 3 chosen by a TSO. The TSO might profile by choosing only dark-skinned young men. (Whether or not this is acceptable/desirable is up to your personal ethics.) Or they might choose targets that are unlikely to protest, like young mothers with children or elderly people. Or the TSO might randomly choose "cuties" and "hotties". I've heard reports of all three.