#2 is called this: http://en.wikipedia.org/wiki/Buffon%27s_needle http://en.wikipedia.org/wiki/Buffon%27s_needle. This is also mentioned in Jordan Ellenberg's b

#2 is called this: http://en.wikipedia.org/wiki/Buffon%27s_needle http://en.wikipedia.org/wiki/Buffon%27s_needle. This is also mentioned in Jordan Ellenberg's book How Not to Be Wrong, and has a similar passage with your explanation above. I mention the book as much because it's a great read.