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

18
Start Fraction 1 over 8 End Fraction

32
Start Fraction 3 over 2 End Fraction

12
Start Fraction 1 over 2 End Fraction

1216
Start Fraction 1 over 216 End Fraction

Answer 1

To determine the probability of rolling an odd number three times in a row on a number cube (which has faces numbered 1 through 6), we can follow these steps:

1. Identify the odd numbers on a standard number cube: 1, 3, and 5. There are 3 odd numbers.
2. The total number of outcomes when rolling the cube is 6 (since it has 6 faces).
3. The probability of rolling an odd number in one roll is:
\[
P(\text{odd}) = \frac{\text{number of odd numbers}}{\text{total number of outcomes}} = \frac{3}{6} = \frac{1}{2}
\]

4. To find the probability of rolling an odd number three times in a row, we raise the probability of a single roll to the power of the number of rolls:
\[
P(\text{odd three times}) = P(\text{odd})^3 = \left(\frac{1}{2}\right)^3 = \frac{1}{8}
\]

The answer is:

**Start Fraction 1 over 8 End Fraction**