News channels like to talk about crimes and terrorism because these topics create strong emotions. But strong emotions can lead to anxiety, anxiety can lead to depression, depression can lead to death. Note a slippery slope bias here.
Actually it still can happen, but the chances are pretty small. But if anxiety doesn’t usually lead to immediate death, it creates smaller problems for people. Fortunately we can use risk analysis to counter sources of anxiety like news about terrorism. Also we are going to use methods from cognitive therapy, which proposes to replace dysfunctional beliefs with more useful and harmless ones. In this case it would be a belief like this: “acts of terrorism occurs often, we should be afraid.”
We can simplify the utility theory here using only probabilities without any utility values because we are going to compare only probabilities. All the probabilities would be multiplied by the same utility value, so we don’t have to take this value into account.
Let’s compare some probabilities: the chance of dying from cardiovascular disease, the change of dying in a motor vehicle crash, and the chance of dying in a terrorist attack. You can calculate these probabilities for any particular country for even a smaller region like a city. You only need to take a number of residents in the area of interest and a number of deaths from a particular cause during a particular year. Dividing the number of deaths per year by the number of residents you would get a probability you need.
Before going to probabilities of causes of death consider how often these events are mentioned in media. Heart diseases are not widely mentioned, you most likely hear about it only when a celebrity have such a disease or when a pharmaceutical company promotes drugs aimed on people with a disease like this. Motor vehicle crashes could be mentioned more often, because media can ruminate on all gory details to attract audiences while forcing their emotions. The same is true about terrorism, it gets even greater media coverage, then politicians and celebrities talk about it for a while, creating even greater coverage.
You can prove or disprove my own estimations for a region of your choice, but as far as I know the probability of cardiovascular disease is greater than the probability of a motor vehicle accident. The probability of a terrorist act is the lowest. So if you are anxious regarding a possible terrorist attack you can check probabilities and compare them with other causes of death you are not anxious about. Due to disproportionate media coverage of causes of death people often fear ones with lowest probabilities. And fortunately if you become aware of more probably causes of death, media most likely wouldn’t support your anxiety. You can also think about what you can do to decrease the probability of cardiovascular disease, for example. There are some scientifically backed recommendations what people need to do to live a healthier life.