That's only worse than random chance if the base rate of having bombs (among people ending up in Guantanamo Bay, anyway) is more than 1/3. Were you assuming it

That's only worse than random chance if the base rate of having bombs (among people ending up in Guantanamo Bay, anyway) is more than 1/3. Were you assuming it would be 1/2 or something? I don't see any reason to conclude that. I can easily believe that the base rate would be under 1/3, and so 1/3 would in fact be better than random chance.