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) 1/5 1/216 3/2 1/2
Answers
GPT-4o mini
To determine the probability of rolling an odd number on a number cube (which has the numbers 1 through 6), we first identify the odd numbers available on the cube: 1, 3, and 5. There are 3 odd numbers.
The total number of outcomes when rolling a six-sided cube is 6.
Thus, the probability \( P \) of rolling an odd number in a single roll is:
\[
P(\text{odd}) = \frac{\text{Number of odd outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
Since we want to find the probability of rolling an odd number three times in a row, we multiply the probabilities of rolling an odd number for each of the three rolls:
\[
P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8}
\]
However, since this option is not among the provided choices, we recalculate:
In confirming:
- Odd outcomes: 3 ways (1, 3, 5)
- Total outcomes: 6 ways (1-6)
- Probability of odd on one roll: \( \frac{3}{6} = \frac{1}{2} \)
- Probability of getting 3 odd numbers in sequence:
\[
\left( \frac{1}{2} \right)^3 = \frac{1}{8}
\]
Since none of the answers provided correlate with this calculation, I will note that the probable answer is established based on the calculations.
To summarize: The probability of rolling an odd number three times in a row is \( \frac{1}{8} \), which does not match any of your provided choices. If you were looking for an approximation or different calculation method for alternative choices to answer mathematical queries, please note that \( \frac{1}{216} \) could relate to different context and would suggest a different outcome setting.
None of the choices you provided (1/5,1/216, 3/2, 1/2) align with this computation.
Therefore, based on sound calculations, the response to the odd triples on a cube remains \( \frac{1}{8}\).
The total number of outcomes when rolling a six-sided cube is 6.
Thus, the probability \( P \) of rolling an odd number in a single roll is:
\[
P(\text{odd}) = \frac{\text{Number of odd outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
Since we want to find the probability of rolling an odd number three times in a row, we multiply the probabilities of rolling an odd number for each of the three rolls:
\[
P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8}
\]
However, since this option is not among the provided choices, we recalculate:
In confirming:
- Odd outcomes: 3 ways (1, 3, 5)
- Total outcomes: 6 ways (1-6)
- Probability of odd on one roll: \( \frac{3}{6} = \frac{1}{2} \)
- Probability of getting 3 odd numbers in sequence:
\[
\left( \frac{1}{2} \right)^3 = \frac{1}{8}
\]
Since none of the answers provided correlate with this calculation, I will note that the probable answer is established based on the calculations.
To summarize: The probability of rolling an odd number three times in a row is \( \frac{1}{8} \), which does not match any of your provided choices. If you were looking for an approximation or different calculation method for alternative choices to answer mathematical queries, please note that \( \frac{1}{216} \) could relate to different context and would suggest a different outcome setting.
None of the choices you provided (1/5,1/216, 3/2, 1/2) align with this computation.
Therefore, based on sound calculations, the response to the odd triples on a cube remains \( \frac{1}{8}\).