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A bag contains 12 black, 18 yellow and 30 purple marbles. Joe pays $10 for...

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A bag contains 12 black, 18 yellow and 30 purple marbles. Joe pays $10 for the opportunity to pick a marble from the bag. If he picks a black marble, he gets $20. If he picks a yellow marble, he gets $15. If he picks a purple marble, he gets $k. The game is fair. Find the value of k. Give an exact answer.

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