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

1 answer

To determine the probability of rolling an odd number on a number cube (which typically has the faces numbered 1 through 6), we first identify how many faces show odd numbers.

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

The probability of rolling an odd number in one roll is:

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

Now, we want to find the probability of rolling an odd number three times in a row. Since the rolls are independent, we multiply the probabilities for each roll:

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

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

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

Therefore, the correct response is:

18 Start Fraction 1 over 8 End Fraction.