what is the probability of rolling a one on the first die and an even number on the second die? write your…

Explanation:

Step1: Probability of rolling a 1 on first die

The first die has 6 possible outcomes (1 - 6), and rolling a 1 is 1 favorable outcome. So the probability $P_1=\frac{1}{6}$.

Step2: Probability of rolling an even number on second die

The second die also has 6 possible outcomes. Even - numbered outcomes are 2, 4, 6, so there are 3 favorable outcomes. So the probability $P_2 = \frac{3}{6}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since the rolls of the two dice are independent events, the probability of both events occurring is $P = P_1\times P_2$. $P=\frac{1}{6}\times\frac{1}{2}=\frac{1}{12}$

Answer:

$\frac{1}{12}$