To determine the probability of rolling an odd number three times in a row on a standard number cube (which has sides numbered 1 through 6), we first find the probability of rolling an odd number in a single roll.
The odd numbers on a number cube are: 1, 3, and 5. Therefore, there are 3 odd numbers out of 6 total numbers.
The probability \( P \) of rolling an odd number in one roll is:
\[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \]
Now, we want the probability of this event happening three times in a row. Since the rolls are independent, we multiply the probabilities:
\[ P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]
Thus, the probability of rolling an odd number three times in a row is:
\[ \frac{1}{8} \]
So the correct response is:
Start Fraction 1 over 8 End Fraction
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