Consider the following game. A circular target of radius 1 is zoned into 3 concentric disks of radius , , 1. A dart is tossed at random onto the circle. If it lands in the central circular region Rupees 3 is won, if it lands in the outermost annular region Rupee 1 is won and Rupees 2 is won if it lands in between these two regions. Let X denote the amount of money won. Find the expectation of X, correct to three decimal places.