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

Answer:

$\frac{1}{12}$

Explanation:

Step1: Probability of even - number on first die

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

Step2: Probability of 4 on second die

The probability of rolling a 4 on the second die, $P(B)=\frac{1}{6}$.

Step3: Use multiplication rule for independent events

Since the rolls of the two dice are independent events, the probability of both events occurring is $P(A\cap B)=P(A)\times P(B)$. So $P(A\cap B)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}$.