I typed in mountaion lion in Wikipedia just out of curiosity, and here's what it said about attacks on humans:
Due to the expanding human population, cougar ranges increasingly overlap with areas inhabited by humans. Attacks on humans are rare, as cougar prey recognition is a learned behavior and they do not generally recognize humans as prey.[4] Attacks on people, livestock, and pets may occur when the cat habituates to humans or is in a condition of severe starvation. Attacks are most frequent during late spring and summer, when juvenile cougars leave their mothers and search for new territory.[56]
Between 1890 and 1990, in North America there were 53 reported, confirmed attacks on humans, resulting in 48 nonfatal injuries and 10 deaths of humans (the total is greater than 53 because some attacks had more than one victim).[82] By 2004, the count had climbed to 88 attacks and 20 deaths.[83]
Within North America, the distribution of attacks is not uniform. The heavily populated state of California has seen a dozen attacks since 1986 (after just three from 1890 to 1985), including three fatalities.[55] Lightly populated New Mexico reported an attack in 2008, the first there since 1974.[84]
As with many predators, a cougar may attack if cornered, if a fleeing human stimulates their instinct to chase, or if a person \"plays dead\". Exaggerating the threat to the animal through intense eye contact, loud but calm shouting, and any other action to appear larger and more menacing, may make the animal retreat. Fighting back with sticks and rocks, or even bare hands, is often effective in persuading an attacking cougar to disengage.[4][56]
When cougars do attack, they usually employ their characteristic neck bite, attempting to position their teeth between the vertebrae and into the spinal cord. Neck, head, and spinal injuries are common and sometimes fatal.[4] Children are at greatest risk of attack, and least likely to survive an encounter. Detailed research into attacks prior to 1991 showed that 64% of all victims?and almost all fatalities?were children. The same study showed the highest proportion of attacks to have occurred in British Columbia, particularly on Vancouver Island where cougar populations are especially dense.[82] Preceding attacks on humans, cougars display aberrant behavior, including: active during daylight hours, unafraid of humans, and stalking humans.[85] There have sometimes been incidents of pet cougars mauling people.[86][87]
Just from a little reading, it sounds like the chance of having a problem with one of these things is slightly less than being hit by lightning. What a bad way to go though. One of those things trying to go for your neck.
