Question

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Part 1
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 and a 3 on the second roll of a single die, we can break it down as follows:

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

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

3. **Total probability of both independent events occurring:**
- Since the two rolls of the die are independent events, we multiply their probabilities:
\[
P(\text{5 on 1st and 3 on 2nd}) = P(\text{5 on 1st}) \times P(\text{3 on 2nd}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]

So, the probability of getting a 5 on the first roll and a 3 on the second roll is \(\frac{1}{36}\).