what is the probability of rolling even numbers on both dice? write your answer as a fraction or a whole…

Explanation:

Step1: Determine single - die probability

A standard die has 6 faces numbered from 1 to 6. The even numbers are 2, 4, 6. So the probability of rolling an even number on a single die is $\frac{3}{6}=\frac{1}{2}$.

Step2: Use multiplication rule for independent events

Since the rolls of the two dice are independent events, the probability of two independent events A and B both occurring is $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of rolling an even number on the first die and $B$ is the event of rolling an even number on the second die. So the probability of rolling even numbers on both dice is $\frac{1}{2}\times\frac{1}{2}$.

Answer:

$\frac{1}{4}$