To find the probability of rolling an odd number three times in a row with a number cube (which typically has numbers 1 through 6), we first determine the probability of rolling an odd number in a single roll.
The odd numbers on a standard number cube are 1, 3, and 5. So, there are 3 odd numbers out of a total of 6 possible outcomes.
The probability \( P \) of rolling an odd number in one roll is:
\[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \]
Now, to find the probability of rolling an odd number three times in a row, we multiply the probabilities of each independent event:
\[ P(\text{3 odd numbers}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{8} \]
Therefore, the probability of rolling an odd number three times in a row is:
\[ \frac{1}{8} \]
The corresponding response from your options is:
Start Fraction 1 over 8 End Fraction.