The center of a coin must fall within a triangle. The reasonable assumption is that it is evenly distributed.

Draw a small regular triangle inside the triangle, which is concentric and parallel to the big triangle, and the distance is 1/2.

When the center of a coin falls within a small triangle, the coin will not intersect with a large triangle.

P (coins and big triangles have something in common)? =? 1-P (coins don't intersect with big triangles)?

=? 1- (small triangle area)/(large triangle area)? =? 1-(3-√3)? /3=? 1-0. 1786? =? 0.82 13

{of which:? (small triangle area)/(large triangle area)? =? (3-√3)? /3 is simplified. }