Let's start with definitions:
A Sighting: When someone sees a Mountain Lion but the Lion shows no threatening behavior. May, in fact, walk or run away.
An Encounter: When a Mountain Lion may stare, or stalk, or otherwise threaten someone, but there is no physical contact.
An Attack: When there is physical contact with a Mountain Lion.
An Attack that results in Death: When physical contact results in death of someone.
Now, a word about Sightings. It has been estimated that over 80% of all Mountain Lion Sightings are false. In reality, they are probably deer, bobcats, or coyotes. We had a guest that came running into the main house saying that she saw a Mountain Lion walking down our driveway. I immediately grabbed my camera and went looking. What did I find? An adult full size -- Bobcat. There are a number of possible reasons for the high false rate of "mountain lion" sightings. Most people have never seen a Mountain Lion in the wild. Many have never seen a Bobcat in the wild either. Unless you are familiar with each, it could be easy to mistake one for the other. Mountain Lions are essentially nocturnal, so are not normally out and about during the day. But also, Mountain Lions are camouflage experts, and often one doesn't get to see the entire lion. They are behind cactus or boulders where it is not easy to see them. (I think that is the whole point of the Mountain Lion's behavior, ie. not to be seen). Second, if you think you are seeing a mountain lion, your adrenaline is undoubtedly pumping and so you are not a calm, collected, reliable observer. Third, eyewitness sightings are rare and very brief events -- as little as five seconds. But the most important reason may simply be that humans cannot judge distance well, and when viewed from below an animal can appear much larger. (A 20 pound bobcat can appear to be the size of a 100 pound mountain lion). I know this to be the case because once Christine and I were hiking in Saguaro National Park when we came up over a ridge and both immediately saw what appeared (for a brief second) to be a Deer. However, it was, in fact, a Jackrabbit.
My photo today -- obviously not in the wild, but taken at the Arizona Sonoran Desert Museum here in Tucson:
Now, a word about Probabilities. I have on several occasions gone looking specifically for Mountain Lions. I have gone to places said to have the highest concentration of lions in the state or country -- or province. With one possible exception, I have never seen one in the wild. I say possible for all the reasons explained in the previous paragraph. Christine and I were hiking in Saguaro National Park. One of the trails was closed that morning due to a Mountain Lion that was protecting a kill. So, Christine and I hiked an adjacent trail. On that trail I did see what appeared to be a large mammal walking parallel to us behind a lot of prickly pear cactus and mesquite trees. I never saw the head -- nor the tail which certainly would have helped. I immediately started walking diagonally in that direction but the animal disappeared quickly. The entire event took about 10 seconds at most. Was it a Mountain Lion? Maybe, but then again maybe not. I have come across Mountain Lion tracks many times. Some seemed very fresh and some were not there when I went by that spot an hour earlier. I have often thought that when I die, and appear before St. Peter, the first question I want to ask (other than where are all the pens I've lost) is how many times a Mountain Lion saw me when I didn't see him?
And, finally a word about Dangers. Over the past 30 years the average number of Mountain Lion attacks in the United States and Canada (combined) has been 5.6 per year. The average number of Mountain Lion attacks that resulted in death in the United States and Canada has averaged 0.8 per year (four every five years). To put this in perspective, in the last five years the average number of deaths from domestic dogs (mostly pit bulls and rottweilers) in the United States alone is 29.6 (that's an average per year). Also, on average 1008 people are treated in hospital emergency rooms for dog bites EVERY SINGLE DAY in the United States.
For me, seeing a Mountain Lion in the wild would be thrilling. I would, however, be very cautious and try to keep a safe distance.