Assume you have a sheet of paper made of horizontal and vertical lines, and the distance between parallel lines is $8\ mm$. A circular coin with radius $1\ cm$ is being tossed on the paper. What is the chance that the coin is being intersected by exactly 5 lines (doesn't matter how many are horizontal or vertical).
I found out that if the coin is tangent to exactly one line, it can move perpendicular to that line for $4\ mm$ until the next line is tangent, and it can move parallel to both sides until the lines are tangent to the coin. In other words, the center of the coin can be in a square of area $16\ mm^2$, out of an area of $5.76\ cm^2$.
The problem I am facing that prevents me approving this answer logically, is the total sampling space area.