Question: A large wooden floor is laid with strips 2 inches wide with negligible space between the strips. A uniform circular disk of diameter 2.25 is dropped at random on the floor. What is the probability that the disk touches three of the wooden strips.
My Issue: This is not a homework problem. This is a question in my Actuarial Exam P study guide. I am having trouble visualizing a way to do this problem. I know that the answer is 0.25/2=1/8, but I am having trouble seeing why.
My best thanks in advance
I think I figured it out.
Suppose we have the following 3 boxes, each 2 inches long. x=0_| - - |- - - - - | - - | x=6 so the total length is 6 inches. We know the diameter of the circle is 2.25 inches, so if we draw a horizontal line from 1.75, we will end at 4 which is just touching the last square. If we touch the edge of the first square (x=2), then we end at 4.25=x. If we start our circle any further down, our circle won’t touch the first block. We know x~unif(0,2) so f(x)=1/2 So we are looking for P(1.75(2,1.75)=(2-1.75)/2=1/8
Basically you're picking a random number (location of the center of the disk) out of [0,2] and asking what are the chances it's in [0.875, 1.125].
Because the distribution is uniform and the range is 1/8 out of all possible outcomes, the answer is 1/8.