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

Explanation:

Step1: Probability of rolling a 5 on first die

A die has 6 faces. The probability of rolling a 5 on the first die is $\frac{1}{6}$ since there is only 1 face with a 5 out of 6 possible outcomes.

Step2: Probability of rolling an even number on second die

The even - numbered faces on a die are 2, 4, 6. So there are 3 even - numbered faces out of 6. The probability of rolling an even number on the second die is $\frac{3}{6}=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since the rolls of the two dice are independent events, the probability of both events occurring is the product of their individual probabilities. So $P=\frac{1}{6}\times\frac{1}{2}$. $P = \frac{1\times1}{6\times2}=\frac{1}{12}$

Answer:

$\frac{1}{12}$