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Bonus: (15 points) An archer can hit the bull's-eye of the target with probability 1/3. She shoots until she hits the bull's eye or until

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Bonus: (15 points) An archer can hit the bull's-eye of the target with probability 1/3. She shoots until she hits the bull's eye or until four shots have been taken. The number of shots is observed. Determine the probability distribution for this experiment

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