Every year about one car sized asteroid will hit the Earth and leave a formidable crater. Surely this would be a spectacular and very frightening event to witness. Let’s do the math: how likely it is that one of these asteroids will impact within 0.5 kilometers of your house?
The Earth has a radius of about 6400 kilometers. With the respective formula for a sphere, we can use this value to calculate the surface area of Earth:
S = 4 · π · (6400 km)² = 515 million km²
This is the total area available for the asteroids to hit. A region of radius 0.5 km around your house has the area:
A = π · (0.5 km)² = 0.79 km²
Assuming our car sized asteroid falls randomly onto the surface of Earth, which certainly is a legitimate assumption to make, the chance of the asteroid hitting within half a kilometer of your house (or your current location for that matter) is:
p(hit) = A / S = 1 in 655 million
So it’s amazingly small. But since on average one asteroid of this size will hit per year, the above number only covers your chance over one year. What about the chance of such a hit over the course of a life? We approach this the same way as in the snack “Homicide She Wrote”. We calculate the chance of not being hit 70 times in a row and from that deduce the chance of a hit over a life span:
p(hit 70 years) = 1 in 9 million
You think that’s a low probability? It is, the chance of being struck by lightning is much higher, but tell that to the about 800 people of the 7000 million alive today who, according to the calculated odds, are expected to actually witness such a close asteroid strike at some point in their lives.
(This was an excerpt from my introductory statistics and probability ebook Statistical Snacks)