I'm afraid of being on a plane, or in a public place as was the case with this story, and being the victim of one of these terrorist mass killings (or having a friend/loved one be a victim). Now, I'm not deathly afraid of this, because the chances of it happening to me or someone I know are pretty small (again, based on statistics) - but I'm afraid enough of it that I'm cognizant that it's a non-zero possibility.
The way it should be handled is fairly easy. If there's a certain group of people who have been statistically proven to be more likely to commit these types of crimes (whether it be people who are over 7 feet tall, people with the first name "Peter", or oh say - I dunno - happen to practice the muslim religion), then they should be subject to more strict searches and monitoring. If one of those groups is 37 times more likely to commit an act of terror, then people of that group should be subjected to 37 times as many searches, 37 times as much surveillance/monitoring, etc. Again, just based on math/probability/statistics.