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# NASA satellite fall on Earth: 1-in-3200 chance to hit someone. How so?

Q = 1 - (1 - x/y)^26 = 1/3200,

where

• If we pack all 6 billion human beings into a very compact square area, that area will cover x square miles.
• The total area of the earth is y square miles,
• Q is the chance that at least one out of 26 pieces (expected to fall on earth) hits the square area in question

If this is the case, then the human beings occupy a proportion R = 1 - {1 - 1/3200}^(1/26) of the surface of the earth, which is about 1/100,000.

What if instead of hitting one human being, we change problem to falling less than 20 centimeters away from one human being? This is an interesting coverage problem in the theory of statistics. And the damage from a 1 kg of iron hitting earth at 5 miles per second is probably as bad if it falls 20 centimeters away from you, than directly on you.

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Comment by Vincent Granville on September 23, 2011 at 2:05pm
Would be nice to have hourly update on that 1/3200 probability. I'm sure Saturday we'll see thousands of people selling satellite debris on eBay for hundreds of dollars.