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.]
(c) Find the probability P(A|B).
(d) Are events A and B independent? Why?