There are something like 25k flights per day in the US. If each one averages 2.5 hours gate to gate, that's something like 62,500 flight hours. Assuming an eight hour shift, and assuming (absurdly) zero down time between flights, you'd need something like eight thousand FAMs on duty every day, or about 12k in total. TSA won't release numbers, but I haven't seen an estimate over 4k, and most are 1-2k. So, figure the odds of a given flight having a FAM at well under 10%.