Question

A single die is rolled twice. Find the probability of getting a 5 the first time and a 3 the second time.

Answer 1

To find the probability of rolling a 5 on the first roll of a die and a 3 on the second roll, we need to consider the probabilities of each individual event.

1. The probability of rolling a 5 on the first roll of a die:
- There is 1 favorable outcome (rolling a 5) out of 6 possible outcomes (1, 2, 3, 4, 5, 6). Thus, the probability is:
\[
P(\text{5 on first roll}) = \frac{1}{6}
\]

2. The probability of rolling a 3 on the second roll of a die:
- Similarly, there is 1 favorable outcome (rolling a 3) out of 6 possible outcomes. Thus, the probability is:
\[
P(\text{3 on second roll}) = \frac{1}{6}
\]

3. Since the rolls are independent (the outcome of one roll does not affect the other), we can multiply the probabilities of the two independent events:
\[
P(\text{5 on first roll and 3 on second roll}) = P(\text{5 on first roll}) \times P(\text{3 on second roll}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]

Therefore, the probability of rolling a 5 on the first roll and a 3 on the second roll is:
\[
\boxed{\frac{1}{36}}
\]