Question
A fair number cube is labeled 1-6. A student rolls the number cube two times.
What is the probability that the student gets an odd number both times
What is the probability that the student gets an odd number both times
Answers
GPT-4o mini
To find the probability of rolling an odd number both times with a fair number cube (dice) labeled from 1 to 6, we first identify the odd numbers available on the cube.
The odd numbers on a standard number cube are 1, 3, and 5. Therefore, there are 3 odd outcomes.
The probability of rolling an odd number in a single roll of the dice is calculated as:
\[
\text{Probability of rolling an odd number} = \frac{\text{Number of odd outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
Since the two rolls are independent events, the probability of rolling an odd number on both rolls is the product of the probabilities of rolling an odd number on each roll:
\[
\text{Probability of rolling odd both times} = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{4}
\]
Therefore, the probability that the student gets an odd number both times is \(\frac{1}{4}\).
The odd numbers on a standard number cube are 1, 3, and 5. Therefore, there are 3 odd outcomes.
The probability of rolling an odd number in a single roll of the dice is calculated as:
\[
\text{Probability of rolling an odd number} = \frac{\text{Number of odd outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
Since the two rolls are independent events, the probability of rolling an odd number on both rolls is the product of the probabilities of rolling an odd number on each roll:
\[
\text{Probability of rolling odd both times} = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{4}
\]
Therefore, the probability that the student gets an odd number both times is \(\frac{1}{4}\).