To determine the probability of rolling an odd number on a standard six-sided number cube (die) three times in a row, we first need to identify the odd numbers on the cube. The odd numbers on a die are 1, 3, and 5.
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Identify the total outcomes: A standard six-sided die has 6 faces (1, 2, 3, 4, 5, 6).
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Identify the favorable outcomes: The odd numbers are 1, 3, and 5, which gives us 3 favorable outcomes.
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Calculate the probability of rolling an odd number once: \[ P(\text{Odd}) = \frac{\text{Number of odd outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} \]
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Calculate the probability of rolling an odd number three times in a row: Since the rolls are independent, we can multiply the probabilities: \[ P(\text{Odd three times}) = P(\text{Odd}) \times P(\text{Odd}) \times P(\text{Odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{8} \]
Therefore, the probability of rolling an odd number three times in a row is:
\[ \frac{1}{8} \]
The correct answer is:
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