I'm studying an introductory statistics textbook and, unfortunately, it doesn't come with an answer key. The textbook gave this problem, which I've spending hours trying to figure out:
"Roll two fair dice separately. Each die has six faces.
a. List the sample space.
b. Let A be the event that either a three or four is rolled first, followed by an even number. Find P(A).
c. Let B be the event that the sum of the two rolls is at most seven. Find P(B).
d. Find P(A|B)."
My answers to questions b and c are P(A) = $\frac{6}{36}$ and P(B) = $\frac{21}{36}$. I can't for the life of me figure out how to calculate P(A|B) since I don't know if the events are dependent in which I would be using the formula P(A|B) = $\frac{P(A \cap B)}{P(B)}$ or if they're independent meaning I would then be using the formula P(A|B) = P(A)P(B). Can someone please explain how I would go about calculating this problem?