To find the probability of rolling a 2 on a standard 6-sided die both times, follow these steps:
1. Determine the probability of rolling a 2 on one roll of the die:
- A standard 6-sided die has the numbers 1, 2, 3, 4, 5, and 6.
- There is only one 2 on the die.
- Therefore, the probability of rolling a 2 in one roll is [tex]\(\frac{1}{6}\)[/tex].
2. Calculate the probability of rolling a 2 both times:
- Rolling the die twice are independent events. The outcome of the first roll does not affect the outcome of the second roll.
- The probability of both independent events happening is the product of their individual probabilities.
- Hence, the probability of rolling a 2 on the first roll is [tex]\(\frac{1}{6}\)[/tex], and the probability of rolling a 2 on the second roll is also [tex]\(\frac{1}{6}\)[/tex].
- Multiply these probabilities:
[tex]\[
\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\][/tex]
Thus, the probability of rolling a 2 both times is [tex]\(\frac{1}{36}\)[/tex].
