To determine the probability of rolling an odd number three times in a row on a standard number cube (which has faces numbered 1 through 6), we first identify the odd numbers on the cube. The odd numbers are 1, 3, and 5.
There are a total of 6 faces on the cube, and 3 of them are odd. Therefore, the probability of rolling an odd number in a single roll is:
\[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \]
To find the probability of rolling an odd number three times in a row, we multiply the probability of rolling an odd number for each of the three rolls:
\[ P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]
Now, looking at the response options, the answer should be \( \frac{1}{8} \).
However, it seems that the provided options do not include \( \frac{1}{8} \). The closest and most logical option is:
\[ \text{None of the provided options are correct.} \]
If you have to select from the given options, review the numbers for potential typographical errors or misunderstandings in the problem statement.
1 answer