Two distinguishable fair dice are rolled. Define the following events: A={sum of the numbers rolled is odd} B ={sum of the numbers rolled is greater than 8} Are events A and B independent? Justify your answer.
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1. Two distinguishable (so order matters) fair dice are rolled. Define the following events: A = {sum of the numbers rolled is odd}, B = {sum of the numbers rolled is greater than 8}. (a) Find the probabilities P(A) and P(B). [Hint: First define events A and B explicitly, as a list of all outcomes in an event.] (b) Find the probabilities P(A ∪ B) and P(A ∩ B). [Hint: First define events A ∪ B and A ∩ B explicitly, as a list of all outcomes in an event.] (c) Are events A and B independent? Why?
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