Question

a single die is rolled twice. find the probability of rolling an even number the first time and a number greater than 5 the second time.

find the probability of rolling an even number the first time and a number greater than 5 the second time.

\boxed{} (type an integer or a simplified fraction.)

Explanation:

Step1: Probability of even first roll

A die has 6 faces (1 - 6). Even numbers: 2, 4, 6 (3 outcomes). So \( P(\text{even}) = \frac{3}{6}=\frac{1}{2} \).

Step2: Probability of >5 second roll

Numbers >5 on a die: only 6 (1 outcome). So \( P(>5) = \frac{1}{6} \).

Step3: Multiply probabilities (independent events)

Since rolls are independent, \( P(\text{even and } >5) = P(\text{even}) \times P(>5) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \).

Answer:

\(\frac{1}{12}\)