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Concentric circles of radius 1inch and 3 inches are drawn on a circular target of radius 5 inches as shown below. A person fires at the target and receives 10 points, 5 points, or 3 points according to whether the target is hit inside the smaller circle, inside the middle annular region, or inside the outer annular region, respectively. Suppose the person hits the target with probability 0.5, and then is just as likely to hit one point of the target as the other. Find the number of points a person is expected to score each time he or she fires. (Please see the attached file)


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