Consider an experiment that involves rolling a fair six-sided die twice. Let X denote the number rolled on the rst roll and let Y denote the number on the second. (a) How many possible outcomes are there? That is, how many di erent observed values for (X; Y ) can eventuate from this experiment? (Just an answer is okay if you know it). (b) For the remainder of this question you may assume that these outcomes are all equally likely to occur. What is the probability associated with each outcome occurring? (c) Let A denote the event that the sum of the two numbers rolled is greater than 10 (i.e. X + Y > 10). Calculate the probability of event A occurring. (d) What is the probability of A not occurring? (e) Now, let B denote the event that at least one of the numbers rolled is a 5. Calculate the probability of event B occurring. (f) Are events A and B mutually exclusive? Explain. (g) Calculate the following: i. The probability that both event A and event B occur. ii. The probability that either event A or event B occurs (this includes the possibility of both occurring). (h) Using one of the probabilities in part (g) above, calculate the probability of neither event A or B occurring. That is, calculate the event that both A and B do not occur at the same time.