(a) To find \(P(A \cap B)\), we need to determine the outcomes where the score on the red die is divisible by 3 and the sum of the two scores is at least 9.

The possible scores on the red die that are divisible by 3 are 3 and 6.

\(For red die = 3, the possible outcomes for the blue die to make the sum at least 9 are: (3,6).\)

\(For red die = 6, the possible outcomes for the blue die to make the sum at least 9 are: (6,3), (6,4), (6,5), (6,6).\)

Thus, the favorable outcomes are: (3,6), (6,3), (6,4), (6,5), (6,6).

There are 5 favorable outcomes out of 36 possible outcomes, so \(P(A \cap B) = \frac{5}{36}\).

(b) To determine if \(A\) and \(B\) are independent, we check if \(P(A) \times P(B) = P(A \cap B)\).

\(P(A) = \frac{2}{6} = \frac{1}{3}\) since the red die can be 3 or 6.

\(P(B) = \frac{10}{36} = \frac{5}{18}\) since there are 10 outcomes where the sum is at least 9.

\(P(A) \times P(B) = \frac{1}{3} \times \frac{5}{18} = \frac{5}{54}\).

Since \(\frac{5}{54} \neq \frac{5}{36}\), events \(A\) and \(B\) are not independent.