Question

You are rolling a number cube to help you pick the number of minutes you will run in each of your workout sets. Determine the probability of rolling an odd number three times in a row.(1 point)
Responses

12
1
2
Start Fraction 1 over 2 End Fraction

32
3
2
Start Fraction 3 over 2 End Fraction

1216
1
216
Start Fraction 1 over 216 End Fraction

18

Answer 1

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.