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The probability is one-half. If you look at the picture of the Push Penny board, you'll notice that the shaded strips are one diameter wide, and the unshaded strips are also one diameter wide:
 
This means that, if the game is random, it is just as likely for the coin to land on a shaded strip as on an unshaded strip. This makes the probability of hitting a line (and landing on a shaded strip) equal to one-half, or 50%.
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