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 1216 Start Fraction 1 over 216 End Fraction 18 Start Fraction 1 over 8 End Fraction 32 Start Fraction 3 over 2 End Fraction 12

Answer 1

To determine the probability of rolling an odd number three times in a row on a standard number cube (a six-sided die), we first identify the odd numbers on the die. The odd numbers on a number cube (1 to 6) are 1, 3, and 5.

There are a total of 3 odd numbers out of 6 possible outcomes. Thus, the probability of rolling an odd number in one roll is:

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

Now, to find the probability of rolling an odd number three times in a row, we use the multiplication rule of probability, since the rolls are independent events:

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

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

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

So the correct answer is:

\[
\text{Start Fraction 1 over 8 End Fraction}
\]