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The probability of picking a dime on each draw is 1/3.
The probability of not picking a dime on each draw is 2/3.
To find the probability of picking a dime exactly twice, we can use the formula for the probability of independent events.
(1/3) * (1/3) * (2/3) = 2/27
Therefore, the probability that a dime is picked exactly twice is 2/27 or approximately 0.074.
So, the answer is not provided among the options.