To find the probability of rolling an odd number on a standard number cube (which has the numbers 1 through 6) three times in a row, we first need to determine the probability of rolling an odd number on a single roll.
The odd numbers on a cube are 1, 3, and 5, which means there are 3 odd numbers out of a total of 6 possible outcomes.
The probability of rolling an odd number on one roll is:
\[ P(\text{odd}) = \frac{\text{number of odd outcomes}}{\text{total outcomes}} = \frac{3}{6} = \frac{1}{2} \]
Next, we are interested in the probability of rolling an odd number three times in a row. Since the rolls are independent, we can multiply the probabilities of each individual roll:
\[ P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]
Thus, the probability of rolling an odd number three times in a row is \(\frac{1}{8}\).
The answer is:
\(\frac{1}{8}\) (which corresponds to the option provided).