I’m a late 20s clean-cut white guy; I travel alone, and a lot, and with usually just my messenger bag — I also get bomb checked every time I fly internationally from Australia!
When I'm not tested, then there is typically another group being tested. They seem to utilize the testing machinery/staff close to 100% of the time, so if you're the next group of people as their finishing up, you're likely to be tested.
Not to say there isn't any bias, but I've never noticed a larger proportion of dark skinned/long haired/bearded etc. individuals being tested vs the departing passenger population.
I travel often and the Australian airports certainly seem to test a much higher percentage of departing passengers than other airports.
I actually have a theory, which is that I (and yourself, and the GP) are targeted to provide deniability of racial profiling. Build up a buffer of whiter-than-white business guys and then no-one can accuse you of racism when you grab the person you really want. No idea if there's any truth to it but it's the only reason I could come up with.
First, it would be random, with no profiling. Profiling gets defeated by shaving, change of clothing, etc. Random selection can't be defeated.
I would make it resistant to implicit profiling from the operators by saying "wear a watch, every time the seconds reach 0 you select the next person for screening."
Then, I would make it hard to dodge being selected by varying pace through screening, with a rule that "at the selection time you pick the next person through the metal detector, without giving passengers any indication that you've picked, and wait for your selectee who gets screened no matter how much they dawdle or how long the X-ray search takes".
Next time you fly you'll observe that the ETD procedure at Australian airports is consistent with this theoretical design.
Fortunately they let you skip the hand-baggage inspection queue if you get inspected, so I’m usually happy to let them as it saves a good 15-20 mins.