Question

Ralph rolls a singls dis two times in a row. What is the probability that he will roll a "thres" both times?

Answer 1

To find the probability that Ralph will roll a "three" both times when rolling a single die twice, we can follow these steps:

1. **Determine the probability of rolling a "three" on one roll:** A standard die has six faces numbered from 1 to 6. Therefore, the probability of rolling a "three" on a single roll is:

\[
P(\text{three on one roll}) = \frac{1}{6}
\]

2. **Determine the probability of rolling a "three" on two consecutive rolls:** Since the rolls are independent events, the probability of both events happening (rolling a "three" first and rolling a "three" second) is the product of their individual probabilities:

\[
P(\text{three on first roll and three on second roll}) = P(\text{three on first roll}) \times P(\text{three on second roll})
\]
\[
P(\text{three on both rolls}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]

Thus, the probability that Ralph rolls a "three" both times is \(\frac{1}{36}\).