3. Consider an experiment that firstly involves rolling a fair six-sided die once and then secondly rolling a fair eight-sided die once. Let X denote the number rolled on the first roll and let Y denote the number rolled on the second roll.

(a) How many possible outcomes are there? That is, how many different observed values for (X, Y ) can eventuate from this experiment? Explain how you got your answer.

(b) For the remainder of this question you may assume that the different observed values (outcomes) for (X, Y ) are all equally likely to occur. What is the probability associated with each outcome occuring?

(c) Let A denote the event that the sum of the two numbers rolled is in between 9 and 11 both inclusive (i.e. 9 X + Y 11). Calculate the probability of event A occurring. Show workings.

(d) What is the probability of A not occurring? Show workings.

(e) Now, let B denote the event that the number rolled on the second roll is exactly 2 digits greater than the number rolled on the first roll (i.e. Y = X + 2) Calculate the event B of occurring