1. Suppose you roll two fair four-sided dice. Let X1 and X2 denote the number of dots that appear on die 1 and die 2 respectively. Let A be the event X1 > 2. Let B denote the event X2 > X1.
a). Find the P(A) and P(B)?
b). Given that event B has occurred, what is the probability that event A has occurred? What is the probability that event A did not occur?
Show your work in detail.