Two ordinary fair dice, one red and the other blue, are thrown.

Event \(A\) is 'the score on the red die is divisible by 3'.

Event \(B\) is 'the sum of the two scores is at least 9'.

(a) Find \(P(A \cap B)\).

(b) Hence determine whether or not the events \(A\) and \(B\) are independent.