Question

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
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1216
Start Fraction 1 over 216 End Fraction

12
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32
Start Fraction 3 over 2 End Fraction
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Answer 1

To determine the probability of rolling an odd number on a standard six-sided number cube (die) three times in a row, we first need to identify the odd numbers on the cube. The odd numbers on a die are 1, 3, and 5.

1. **Identify the total outcomes**: A standard six-sided die has 6 faces (1, 2, 3, 4, 5, 6).
2. **Identify the favorable outcomes**: The odd numbers are 1, 3, and 5, which gives us 3 favorable outcomes.

3. **Calculate the probability of rolling an odd number once**:
\[
P(\text{Odd}) = \frac{\text{Number of odd outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]

4. **Calculate the probability of rolling an odd number three times in a row**:
Since the rolls are independent, we can multiply the probabilities:
\[
P(\text{Odd three times}) = P(\text{Odd}) \times P(\text{Odd}) \times P(\text{Odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{8}
\]

Therefore, the probability of rolling an odd number three times in a row is:

\[
\frac{1}{8}
\]

The correct answer is:

**Start Fraction 1 over 8 End Fraction**