A standard number cube (or die) has six faces, numbered from 1 to 6. The odd numbers on the die are 1, 3, and 5. Therefore, there are 3 odd numbers out of a total of 6 numbers.
To find the probability of rolling an odd number, we can use the formula:
\[ P(\text{odd number}) = \frac{\text{number of odd outcomes}}{\text{total outcomes}} = \frac{3}{6} = \frac{1}{2} \]
Now, we want to determine the probability of rolling an odd number three times in a row. Since the rolls are independent events, we can multiply the probabilities together:
\[ P(\text{3 odd numbers}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]
Thus, the probability of rolling an odd number three times in a row is
\[ \frac{1}{8}. \]