To find the probability of obtaining tails when tossing a coin and rolling a 3 on a number cube (which has faces numbered from 1 to 6), we need to calculate the probabilities of each event separately and then multiply them together.
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Probability of getting tails on a coin toss: There are 2 possible outcomes when tossing a coin (heads or 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: There are 6 possible outcomes when rolling a number cube (1 through 6), so the probability of rolling a 3 is: \[ P(\text{rolling a 3}) = \frac{1}{6} \]
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Combined probability: The probability of both events happening (getting tails and rolling a 3) is the product of the two probabilities: \[ P(\text{tails and rolling a 3}) = P(\text{tails}) \times P(\text{rolling a 3}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \]
Therefore, the probability of obtaining tails and rolling a 3 is: \[ \boxed{\frac{1}{12}} \]