Question

This is a problem based on Buffon's needle problem. ( You can Google it)

Suppose that M. Buffon’s floor is covered, not by unit width floor boards, but by a unit grid of square unit tiles. Suppose now that a unit length needle, (that is, a needle whose length is the length of the sides of these tiles), is dropped “randomly” on this floor. Calculate the probability that the needle crosses an edge of a tile. State clearly the probabilistic assumptions you make in order to carry out this calculation.

Answer 1

For parallel line Buffon needle problem the answer is 2/pi. when length of needle = width between lines

This problem is symmetrical for vertical and horizontal axes.

So Prob(intersection) = prob(intersection along x axis) (1- prob(intersection along y axis) )+ (1-prob(intersection along x axis)) * (prob(intersection along y axis)) + prob(intersection along x and y axes)

= (2/pi *(1-2/pi))*2 + 2/pi *2/pi

= 86%