a single die is rolled twice. find the probability of rolling an even number the first time and a number…

Explanation:

Step1: Calculate first - roll probability

A die has 6 sides. Even numbers are 2, 4, 6. So the probability of rolling an even number on the first roll, $P(A)=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate second - roll probability

Numbers greater than 4 on a die are 5, 6. So the probability of rolling a number greater than 4 on the second roll, $P(B)=\frac{2}{6}=\frac{1}{3}$.

Step3: Use multiplication rule for independent events

Since the two rolls are independent events, the probability of both events occurring is $P(A\cap B)=P(A)\times P(B)$. $P(A\cap B)=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$