To find the probability of rolling two 3's when rolling a standard six-sided die twice, follow these steps:
1. Determine the probability of rolling a 3 on a single roll of a six-sided die:
A standard six-sided die has six faces, each showing a different number from 1 to 6. The probability of rolling any specific number, such as a 3, on one roll is therefore:
[tex]\[
P(3) = \frac{1}{6}
\][/tex]
2. Calculate the probability of rolling a 3 on the first roll and a 3 on the second roll:
Since the rolls of the die are independent events, the probability of both events occurring is the product of the probabilities of each event.
So, the probability of rolling a 3 on the first roll and also a 3 on the second roll is:
[tex]\[
P(3, 3) = P(3 \text{ on first roll}) \times P(3 \text{ on second roll}) = \frac{1}{6} \times \frac{1}{6}
\][/tex]
3. Multiply the probabilities:
[tex]\[
P(3, 3) = \frac{1}{6} \times \frac{1}{6} = \frac{1 \times 1}{6 \times 6} = \frac{1}{36}
\][/tex]
So, the probability of rolling two 3's is:
[tex]\[
P(3, 3) = \frac{1}{36}
\][/tex]
