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

1/8


1/216


1/2


3/2

Answer 1

To determine the probability of rolling an odd number on a standard number cube (which has faces numbered 1 through 6), we first need to identify the odd numbers on the cube. The odd numbers are 1, 3, and 5.

1. **Calculate the number of odd numbers**: There are 3 odd numbers (1, 3, 5) out of a total of 6 numbers on the cube.

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

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

Thus, the probability of rolling an odd number three times in a row is **1/8**.

The correct response is:
**1/8**