How do I solve this problem?

Question

A checkerboard measures 12 inches by 12 inches. There are 8 squares to a side and the checker measures 1 inch in diameter. What is the probability that if someone threw a checker onto the board that it would not be touching a line?

Answer 1

Hi Barb

Let each square is L" on a side, let the diameter if the checker be D.  If you consider the area in a L" square where if the checker landed it would not be crossing or touching a boundary it would be a square whose side would be L-D. If the checker landed any where inside this square it would not touch a line. To picture this make a sketch of two concentric squares the outer one with side L and the inner one with side L-D. 

So the probability is  the ratio of the two areas p(not land on a line) =(L-D)²/L²  L=1.5" and D=1" so p=(.5/1.5)² =.1111 or about 11.1%.

 

Regards

Jim