Two ordinary fair dice are rolled. Event X is the product of the two numbers obtained is

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Two ordinary fair dice are rolled.

Event X is ‘the product of the two numbers obtained is odd’.

Event Y is ‘the sum of the two numbers obtained is a multiple of 3’.

a. Determine, giving reasons for your answer, whether X and Y are independent.

b. Are events X and Y mutually exclusive? Justify your answer.

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