I still dont understand?? If you get tested randomly you could still get tested "randomly" once a day and it would show up
It's a stupid idea and I doubt that anyone has ever used that as rationale to try harder drugs because people don't just generally seek out inebriation regardless of the effects.
But the concept has a real basis behind it:
Imagine a situation in which there is a weekend drug user who uses a drug twice a week, say on Saturday and Sunday. With Marijuana, it would take about 8 days to completely pass all the THC from that first use, but this user uses it again after only 6 days. So that leaves 2/8 or 25% of the THC still stored from the first session there when he tokes up again. By the third week, this has increased to 5/16ths, fourth week is 21/64, etc. To find the total percentage of all THC consumed at the beginning of each cycle we can find the sum at week
n using
Sn = ((1/4)(1-(1/4)n))/(1-(1/4)) to get a percentage of overall THC consumed still held in fat. But anyway, the point is the user will always test positive as long as they keep their habit.
Now let's imagine a drug like cocaine. Aside from the fact that the highs are completely different, cocaine only lasts 2 days in urine. So the same consumption habit on Saturday and Sunday will mean that you will test positive for cocaine only during Sat, Sun, Mon, Tue. So as long as the drug test occurs on Wed, Thur, or Fri, (a 3/7 chance) you'll be negative for any drug use. If you were to use only on Friday after work (assuming it's work that drug tests you), the cocaine would be out of your system by Monday, when you could be tested again, leaving a very small chance of testing positive at work.
