Question

a die is rolled twice. what is the probability rolling a 1 first, followed by rolling an even number? leave your answer as a reduced fraction.

Explanation:

Step1: Probability of rolling a 1

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

Step2: Probability of rolling an even number

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

Step3: Use the multiplication rule for independent events

Since the two rolls of the die 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:

$\frac{1}{12}$