What are the odds of a bigtime asteroid hitting the Earth a la Armageddon and Deep Impact?
Earth along with other planets of the solar system have shown no evidence of large impacts in the last several billion years with impactors larger than about 10 km or so maybe up to 20 or 30 max. Similar size to the one that brought an end to the dinosaur era. However, some planets such as Mars, Mercury and even the moon have many very large craters on the surface indicating that giant asteroid as large as in the movies or larger, but are all well over three billion years old. Since then, earth only received asteroids of approximately 10km, occasionally a bit larger. But these are also extremely unlikely. The largest ones happen once every hundred million years, so that’s a one in a million chance of it happening this century. A one in a million probability is usually thought of as “negligible”.
As time passes the number of large asteroids per unit volume in the universe decreases for two major reasons. Firstly, the universe expands meaning that less number of asteroids will be in the same amount of space. Secondly, asteroids continuously collide with planets and stars and merging with them or splitting into smaller pieces and hence the overall average size of asteroids decrease. As a result the probability that a large asteroid hits the earth decreases.
 (Wikipedia, 2015) http://circanews.com/news/enormous-asteroid-impact-boiled-oceans
(Nasa, 2015) http://neo.jpl.nasa.gov/risks/v
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