To determine the probability of getting a 2 on both dice when rolling two six-sided dice, follow these steps:
1. Calculate the probability of getting a 2 on one die:
Each die has 6 faces, numbered from 1 to 6.
The chance of rolling a specific number, such as 2, is:
[tex]\[
\text{Probability of getting a 2 on one die} = \frac{1}{6}
\][/tex]
2. Determine the probability of both events occurring:
Since the rolls of the two dice are independent events, the probability of both dice showing 2 is the product of their individual probabilities.
[tex]\[
\text{Probability of getting a 2 on the first die and a 2 on the second die} = \left( \frac{1}{6} \right) \times \left( \frac{1}{6} \right)
\][/tex]
3. Multiply the probabilities:
[tex]\[
\left( \frac{1}{6} \right) \times \left( \frac{1}{6} \right) = \frac{1}{36}
\][/tex]
Therefore, the probability of getting a 2 on both dice is [tex]\(\frac{1}{36}\)[/tex].
The correct answer is:
D. [tex]\(\frac{1}{36}\)[/tex]
