Question

A single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 1 the second time.

Answer 1

To find the probability of rolling an even number on the first roll and a number greater than 1 on the second roll with a single die, let's break down the problem:

1. **Determine the outcomes for each roll:**
- A standard die has six faces showing the numbers 1, 2, 3, 4, 5, and 6.

2. **Calculate the probability of rolling an even number on the first roll:**
- The even numbers on a die are 2, 4, and 6.
- There are 3 even numbers out of a total of 6 possible outcomes.

\[
P(\text{even on first roll}) = \frac{3}{6} = \frac{1}{2}
\]

3. **Calculate the probability of rolling a number greater than 1 on the second roll:**
- The numbers greater than 1 on a die are 2, 3, 4, 5, and 6.
- There are 5 numbers greater than 1 out of a total of 6 possible outcomes.

\[
P(\text{number > 1 on second roll}) = \frac{5}{6}
\]

4. **Calculate the combined probability:**
- Since the two rolls are independent events, the total probability can be found by multiplying the probabilities of each event.

\[
P(\text{even on first roll and number > 1 on second roll}) = P(\text{even on first roll}) \times P(\text{number > 1 on second roll}) = \frac{1}{2} \times \frac{5}{6}
\]

\[
= \frac{5}{12}
\]

Thus, the probability of rolling an even number the first time and a number greater than 1 the second time is

\[
\boxed{\frac{5}{12}}.
\]