When a cougar wanders into a city in the West, the policy for most wildlife management agencies is to euthanize the animal. The reason: "When a lion comes into a heavily populated area like this one, there is the potential for something to happen" (South Dakota GF&P Wildlife Manager). Although cougar attacks on humans do take place, they rarely (if ever) take place in heavily populated areas. Moreover, death from cougar attack averages less the 1 per year. Pretty good odds. Here is a list of the 10 ten causes of death not realated to illness or disease (according to the National Center for Health Statistics) that you are much, much more likely.
1) Unintentional Motor Vehicle Traffic, 2) Unintentional Poisoning, 3) Unintentional Fall, 4) Suicide by Firearm, 5) Homicide by Firearm, 6) Suicide Suffocation, 7) Unintentional Unspecified (whatever that means), 8) Suicide Poisoning, 9) Unintentional Suffocation, and 10) Unintentional Drowning.
You are about 43,000 times more likely to die from a traffic collision than you are from a cougar attack. I have yet to hear a case of the Department of Motor Vehicles euthanizing bad drivers, though.