Question
A floor consists of parallel planks which have a two foot width. A circular disc of
diameter one foot is randomly and uniformly dropped onto the planks. Determine the
probability that the disc does not touch the line between two planks. Determine also
the expected distance from the center of the disc to the closest line between two planks
diameter one foot is randomly and uniformly dropped onto the planks. Determine the
probability that the disc does not touch the line between two planks. Determine also
the expected distance from the center of the disc to the closest line between two planks
Answers
yoyoma
I think that you have given the distance between the two planks to be 2 feet, but I am not quite sure on this one. I think the technique would be to determine the surface area of that disc that would come in contact with the plank upon reaching the floor. I am quite intrigued by this problem, as I thought you would need more information to solve it, but I would like to wait and see how it can be solved.
Steve
Take a look at any web site discussing Buffon's Needle
Reiny
Here is an actual calculation of the problem.
Yours involves 2 feet gaps, he works at 2 inches per gap.
So it will be the same.
http://www.youtube.com/watch?v=Vws1jvMbs64
Yours involves 2 feet gaps, he works at 2 inches per gap.
So it will be the same.
http://www.youtube.com/watch?v=Vws1jvMbs64