Pencil darts. In a game of chance, a circle of radius 3 inches is drawn on a piece of paper that is 8.5 × 11 sq. in. While blindfolded, the student tries to place her pencil tip inside the circle. She wins $3 if she is successful, or loses $1 if unsuccessful. (If she misses the paper altogether, she can try again until she hits the paper.) Assume that when she hits the paper, the location of her pencil tip is Uniformly distributed on the paper's surface. What are her expected winnings/loses in this game?