Two fair dice are rolled lets define the following

Two fair dice are rolled. Let's define the following events:

A = {The English words for the numbers rolled start with the same letter.} ,

B = {The English words for the numbers rolled have the same number of letters.} .

(a) Find the probabilities P(A) and P(B). [Hint: first define events A and B explic- itly, 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.]

(d) Are events A and B independent? Why?

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