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

1216
Start Fraction 1 over 216 End Fraction

12
Start Fraction 1 over 2 End Fraction

32
Start Fraction 3 over 2 End Fraction

Answer 1

To determine the probability of rolling an odd number three times in a row on a standard number cube (which has sides numbered 1 through 6), we first find the probability of rolling an odd number in a single roll.

The odd numbers on a number cube are: 1, 3, and 5. Therefore, there are 3 odd numbers out of 6 total numbers.

The probability \( P \) of rolling an odd number in one roll is:

\[
P(\text{odd}) = \frac{3}{6} = \frac{1}{2}
\]

Now, we want the probability of this event happening three times in a row. Since the rolls are independent, we multiply the probabilities:

\[
P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \left(\frac{1}{2}\right)^3 = \frac{1}{8}
\]

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

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

So the correct response is:

**Start Fraction 1 over 8 End Fraction**