To determine the probability of obtaining tails when tossing a coin and rolling a 3 on a number cube (which is a fair six-sided die), we will calculate the probabilities of each event separately and then multiply them together since these two events are independent.
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Probability of tossing tails: A coin has two sides (heads and tails), so the probability of getting tails is:
\[ P(\text{tails}) = \frac{1}{2} \]
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Probability of rolling a 3 on a number cube: A standard number cube has six faces, numbered from 1 to 6. The probability of rolling any specific number (including 3) is:
\[ P(\text{rolling a 3}) = \frac{1}{6} \]
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Combined Probability: Since these two events are independent, we can multiply their probabilities:
\[ P(\text{tails and rolling a 3}) = P(\text{tails}) \times P(\text{rolling a 3}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \]
Thus, the probability of obtaining tails and rolling a 3 is
\[ \boxed{\frac{1}{12}} \]