3 Jason throws two fair dice, each with faces numbered 1 to 6 . Event \(A\) is 'one of the numbers obtained is divisible by 3 and the other number is not divisible by 3 '. Event \(B\) is 'the product of the two numbers obtained is even'.

1. Determine whether events \(A\) and \(B\) are independent, showing your working.
2. Are events \(A\) and \(B\) mutually exclusive? Justify your answer.